-9x^2+36=x^2-8x+16

Solution for -9x^2+36=x^2-8x+16 equation:

-9x^2+36=x^2-8x+16

We move all terms to the left:

-9x^2+36-(x^2-8x+16)=0

We get rid of parentheses

-9x^2-x^2+8x-16+36=0

We add all the numbers together, and all the variables

-10x^2+8x+20=0

a = -10; b = 8; c = +20;
Δ = b2-4ac
Δ = 82-4·(-10)·20
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12\sqrt{6}}{2*-10}=\frac{-8-12\sqrt{6}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{6}}{2*-10}=\frac{-8+12\sqrt{6}}{-20}
$