30^2+x^2=40^2

Solution for 30^2+x^2=40^2 equation:

30^2+x^2=40^2

We move all terms to the left:

30^2+x^2-(40^2)=0

We add all the numbers together, and all the variables

x^2-700=0

a = 1; b = 0; c = -700;
Δ = b2-4ac
Δ = 02-4·1·(-700)
Δ = 2800
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:

$\sqrt{\Delta}=\sqrt{2800}=\sqrt{400*7}=\sqrt{400}*\sqrt{7}=20\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{7}}{2*1}=\frac{0-20\sqrt{7}}{2}
=-\frac{20\sqrt{7}}{2}
=-10\sqrt{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{7}}{2*1}=\frac{0+20\sqrt{7}}{2}
=\frac{20\sqrt{7}}{2}
=10\sqrt{7}
$