9x^2-100=8

Solution for 9x^2-100=8 equation:

9x^2-100=8

We move all terms to the left:

9x^2-100-(8)=0

We add all the numbers together, and all the variables

9x^2-108=0

a = 9; b = 0; c = -108;
Δ = b2-4ac
Δ = 02-4·9·(-108)
Δ = 3888
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:

$\sqrt{\Delta}=\sqrt{3888}=\sqrt{1296*3}=\sqrt{1296}*\sqrt{3}=36\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{3}}{2*9}=\frac{0-36\sqrt{3}}{18}
=-\frac{36\sqrt{3}}{18}
=-2\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{3}}{2*9}=\frac{0+36\sqrt{3}}{18}
=\frac{36\sqrt{3}}{18}
=2\sqrt{3}
$