100=a^2+7^2

Solution for 100=a^2+7^2 equation:

100=a^2+7^2

We move all terms to the left:

100-(a^2+7^2)=0

We get rid of parentheses

-a^2+100-7^2=0

We add all the numbers together, and all the variables

-1a^2+51=0

a = -1; b = 0; c = +51;
Δ = b2-4ac
Δ = 02-4·(-1)·51
Δ = 204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{51}}{2*-1}=\frac{0-2\sqrt{51}}{-2}
=-\frac{2\sqrt{51}}{-2}
=-\frac{\sqrt{51}}{-1}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{51}}{2*-1}=\frac{0+2\sqrt{51}}{-2}
=\frac{2\sqrt{51}}{-2}
=\frac{\sqrt{51}}{-1}
$