4x+36=2x^2-6

Solution for 4x+36=2x^2-6 equation:

4x+36=2x^2-6

We move all terms to the left:

4x+36-(2x^2-6)=0

We get rid of parentheses

-2x^2+4x+6+36=0

We add all the numbers together, and all the variables

-2x^2+4x+42=0

a = -2; b = 4; c = +42;
Δ = b2-4ac
Δ = 42-4·(-2)·42
Δ = 352
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{22}}{2*-2}=\frac{-4-4\sqrt{22}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{22}}{2*-2}=\frac{-4+4\sqrt{22}}{-4}
$