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? Any function that has the form: ax2 + bx + c = 0, where x is a variable which is not known, and a, b, and c are constants. A and b are referred to as coefficients. Additionally, it is worth noting that a cannot be equal to 0 in the equation ax2+bx+c=0. If a is equal to 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.

Finding a solution to a quadratic equation may appear daunting, because both x and x2 are unknown. However, there are a number of methods for solving quadratic equations. One of the most widely used is the quadratic formula. This is the quadratic formula:


When you compute a solution to a quadratic equation, you will always find 2 values for x, 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, these two roots may be equal, resulting in one solution for x.

Quadratic equations are important. Quadratic equations are needed to compute answers to many real-world problems. The acceleration of an object as it falls to earth is one example of an application of quadratic equations.

In our equation, a cannot be zero. However, b can be zero, and so can c.

We this quadratic equation solver is useful to you. We encourage you to plug in different values for a, b, and c. But we totally understand if you just want to use it to find the answers you're looking for. Thank you for your interest in Quadratic-Equation-Calculator.com.

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