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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-4x-12=0

a = 2; b = -4; c = -12;
Δ = b2-4ac
Δ = -42-4·2·(-12)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{7}}{2*2}=\frac{4-4\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{7}}{2*2}=\frac{4+4\sqrt{7}}{4}
$