7x+3=6x^2-6

Solution for 7x+3=6x^2-6 equation:

7x+3=6x^2-6

We move all terms to the left:

7x+3-(6x^2-6)=0

We get rid of parentheses

-6x^2+7x+6+3=0

We add all the numbers together, and all the variables

-6x^2+7x+9=0

a = -6; b = 7; c = +9;
Δ = b2-4ac
Δ = 72-4·(-6)·9
Δ = 265
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{265}}{2*-6}=\frac{-7-\sqrt{265}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{265}}{2*-6}=\frac{-7+\sqrt{265}}{-12}
$