20^2+35^2=x^2

Solution for 20^2+35^2=x^2 equation:

20^2+35^2=x^2

We move all terms to the left:

20^2+35^2-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+1625=0

a = -1; b = 0; c = +1625;
Δ = b2-4ac
Δ = 02-4·(-1)·1625
Δ = 6500
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:

$\sqrt{\Delta}=\sqrt{6500}=\sqrt{100*65}=\sqrt{100}*\sqrt{65}=10\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{65}}{2*-1}=\frac{0-10\sqrt{65}}{-2}
=-\frac{10\sqrt{65}}{-2}
=-\frac{5\sqrt{65}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{65}}{2*-1}=\frac{0+10\sqrt{65}}{-2}
=\frac{10\sqrt{65}}{-2}
=\frac{5\sqrt{65}}{-1}
$