Question

-6x^2=3x+2 How to solve the equation by using the quadratic formula?

Answer 1

Y= -6x² +3x +2

Using the quadratic equation x= $\frac{-b+ \sqrt{b^2-4ac} }{2a}$

We assign variables a,b,c as follows with the form ax²+bx +c

a= -6
b= 3
c=2

By plugging in the variable in the quadratic equation we can find x

$x= \frac{-b+ \sqrt{b^2-4ac} }{2a}$
=$\frac{-3+- \sqrt{3^2-4(-6)(2)} }{2(-6)}$

If you simplify the equation you will have two real solutions for x

$\frac{-3+- \sqrt{9+48} }{-12}$
$\frac{-3+- \sqrt{57} }{-12}$

As a square root can be positive or negative, two solutions are possible
Hence,
$x = \frac{-3+\sqrt{57} }{-12}, \frac{-3- \sqrt{57} }{-12}$

Which can be further simplified to

$x = \frac{\sqrt{57} }{4}, \frac{- \sqrt{57} }{4}$

TAA DAAA! :)
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