100+x^2=324

Solution for 100+x^2=324 equation:

100+x^2=324

We move all terms to the left:

100+x^2-(324)=0

We add all the numbers together, and all the variables

x^2-224=0

a = 1; b = 0; c = -224;
Δ = b2-4ac
Δ = 02-4·1·(-224)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{14}}{2*1}=\frac{0-8\sqrt{14}}{2}
=-\frac{8\sqrt{14}}{2}
=-4\sqrt{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{14}}{2*1}=\frac{0+8\sqrt{14}}{2}
=\frac{8\sqrt{14}}{2}
=4\sqrt{14}
$