x^2=30^2+40^2

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

x^2=30^2+40^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

x^2-2500=0

a = 1; b = 0; c = -2500;
Δ = b2-4ac
Δ = 02-4·1·(-2500)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100}{2*1}=\frac{-100}{2}
=-50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100}{2*1}=\frac{100}{2}
=50
$