x^2+35^2=50^2

Solution for x^2+35^2=50^2 equation:

x^2+35^2=50^2

We move all terms to the left:

x^2+35^2-(50^2)=0

We add all the numbers together, and all the variables

x^2-1275=0

a = 1; b = 0; c = -1275;
Δ = b2-4ac
Δ = 02-4·1·(-1275)
Δ = 5100
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:

$\sqrt{\Delta}=\sqrt{5100}=\sqrt{100*51}=\sqrt{100}*\sqrt{51}=10\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{51}}{2*1}=\frac{0-10\sqrt{51}}{2}
=-\frac{10\sqrt{51}}{2}
=-5\sqrt{51}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{51}}{2*1}=\frac{0+10\sqrt{51}}{2}
=\frac{10\sqrt{51}}{2}
=5\sqrt{51}
$