14^2+x^2=19^2

Solution for 14^2+x^2=19^2 equation:

14^2+x^2=19^2

We move all terms to the left:

14^2+x^2-(19^2)=0

We add all the numbers together, and all the variables

x^2-165=0

a = 1; b = 0; c = -165;
Δ = b2-4ac
Δ = 02-4·1·(-165)
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{165}}{2*1}=\frac{0-2\sqrt{165}}{2}
=-\frac{2\sqrt{165}}{2}
=-\sqrt{165}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{165}}{2*1}=\frac{0+2\sqrt{165}}{2}
=\frac{2\sqrt{165}}{2}
=\sqrt{165}
$