19^2=100+x^2

Solution for 19^2=100+x^2 equation:

19^2=100+x^2

We move all terms to the left:

19^2-(100+x^2)=0

We add all the numbers together, and all the variables

-(100+x^2)+361=0

We get rid of parentheses

-x^2-100+361=0

We add all the numbers together, and all the variables

-1x^2+261=0

a = -1; b = 0; c = +261;
Δ = b2-4ac
Δ = 02-4·(-1)·261
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{29}}{2*-1}=\frac{0-6\sqrt{29}}{-2}
=-\frac{6\sqrt{29}}{-2}
=-\frac{3\sqrt{29}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{29}}{2*-1}=\frac{0+6\sqrt{29}}{-2}
=\frac{6\sqrt{29}}{-2}
=\frac{3\sqrt{29}}{-1}
$