36+x^2+16x+64=36x^2

Solution for 36+x^2+16x+64=36x^2 equation:

36+x^2+16x+64=36x^2

We move all terms to the left:

36+x^2+16x+64-(36x^2)=0

determiningTheFunctionDomain
x^2-36x^2+16x+36+64=0

We add all the numbers together, and all the variables

-35x^2+16x+100=0

a = -35; b = 16; c = +100;
Δ = b2-4ac
Δ = 162-4·(-35)·100
Δ = 14256
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:

$\sqrt{\Delta}=\sqrt{14256}=\sqrt{1296*11}=\sqrt{1296}*\sqrt{11}=36\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-36\sqrt{11}}{2*-35}=\frac{-16-36\sqrt{11}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+36\sqrt{11}}{2*-35}=\frac{-16+36\sqrt{11}}{-70}
$