9x^2=9x^2+36-x^2+100

Solution for 9x^2=9x^2+36-x^2+100 equation:

9x^2=9x^2+36-x^2+100

We move all terms to the left:

9x^2-(9x^2+36-x^2+100)=0

We get rid of parentheses

9x^2-9x^2+x^2-36-100=0

We add all the numbers together, and all the variables

x^2-136=0

a = 1; b = 0; c = -136;
Δ = b2-4ac
Δ = 02-4·1·(-136)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{34}}{2*1}=\frac{0-4\sqrt{34}}{2}
=-\frac{4\sqrt{34}}{2}
=-2\sqrt{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{34}}{2*1}=\frac{0+4\sqrt{34}}{2}
=\frac{4\sqrt{34}}{2}
=2\sqrt{34}
$