Solving 3x2+54x+76 using the Quadratic Formula

A free quadratic equation calculator that shows and explains each step in solving your quadratic equation.


For your equation of the form "ax2 + bx + c = 0," enter the values for a, b, and c:

a
 
x2
 
+
b
 
x
 
+
c
 
= 0
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You entered:
3x2+54x+76=0.

There are two real solutions: x = -1.5389902381335, and x = -16.461009761866.

Here's how we found that solution:

You entered the following equation:
(1)           3x2+54x+76=0.

For any quadratic equation ax2 + bx + c = 0, one can solve for x using the following equation, which is known as the quadratic formula:
(2)          

In the form above, you specified values for the variables a, b, and c. Plugging those values into Eqn. 1, we get:
(3)           \(x=-54\pm\frac{\sqrt{54^2-4*3*76}}{2*3}\)

which simplifies to:
(4)           \(x=-54\pm\frac{\sqrt{2916-912}}{6}\)

Now, solving for x, we find two real solutions:
\(x=\frac{-54+44.766058571199}{6}\) = -1.5389902381335,
  and
\(x=\frac{-54-44.766058571199}{6}\) = -16.461009761866,

Both of these solutions are real numbers.
These are the two solutions that will satisfy the quadratic equation 3x2+54x+76=0.






Notes

What is a quadratic equation? A quadratic equation is an equation that can take the form: ax2 + bx + c = 0, where a, b, and c are constants. X is an unknown. A and b are referred to as coefficients. Further, it is worth pointing out that a cannot equal 0. If a is 0, then ax2=0, and the equation becomes 0+bx+c=0, or bx+c=0. The equation bx+c=0 is a linear equation, and not a quadratic equation.

Solving a linear equation is fairly simple. Solving a quadratic equation is not quite so straightforward. Fortunately, any quadratic equation can reliably be solved using the quadratic formula. This is the quadratic formula:


Solving a quadratic equation will always result in 2 solutions for x. These solutions are called roots. These roots may both be real numbers or, they may both be complex numbers. Depending on the values of a, b, and c, both roots may be the same, producing one solution for x.

Quadratic equations are important. Quadratic equations are needed to compute answers to many real-world problems. For example, to compute whether a braking car can stop fast enough to avoid hitting something would require the use of s quadratic equation.

The quadratic equation calculator on this website uses the quadratic formula to solve your quadratic equations, and this is a reliable and relatively simple way to do it. But there are other ways to solve a quadratic equation, such as completing the square or factoring.

We this quadratic equation calculator is useful to you. We hope the explanations showing how you can solve the equation yourself are educational and helpful. But, if you just want to use it to calculate the answers to your quadratic equations, that's cool too. Thank you for using Quadratic-Equation-Calculator.com.

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