x^2=70^2+120^2

Solution for x^2=70^2+120^2 equation:

x^2=70^2+120^2

We move all terms to the left:

x^2-(70^2+120^2)=0

We add all the numbers together, and all the variables

x^2-19300=0

a = 1; b = 0; c = -19300;
Δ = b2-4ac
Δ = 02-4·1·(-19300)
Δ = 77200
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:

$\sqrt{\Delta}=\sqrt{77200}=\sqrt{400*193}=\sqrt{400}*\sqrt{193}=20\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{193}}{2*1}=\frac{0-20\sqrt{193}}{2}
=-\frac{20\sqrt{193}}{2}
=-10\sqrt{193}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{193}}{2*1}=\frac{0+20\sqrt{193}}{2}
=\frac{20\sqrt{193}}{2}
=10\sqrt{193}
$