31^2+x^2=144^2

Solution for 31^2+x^2=144^2 equation:

31^2+x^2=144^2

We move all terms to the left:

31^2+x^2-(144^2)=0

We add all the numbers together, and all the variables

x^2-19775=0

a = 1; b = 0; c = -19775;
Δ = b2-4ac
Δ = 02-4·1·(-19775)
Δ = 79100
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:

$\sqrt{\Delta}=\sqrt{79100}=\sqrt{100*791}=\sqrt{100}*\sqrt{791}=10\sqrt{791}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{791}}{2*1}=\frac{0-10\sqrt{791}}{2}
=-\frac{10\sqrt{791}}{2}
=-5\sqrt{791}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{791}}{2*1}=\frac{0+10\sqrt{791}}{2}
=\frac{10\sqrt{791}}{2}
=5\sqrt{791}
$