65^2=33^2+x^2

Solution for 65^2=33^2+x^2 equation:

65^2=33^2+x^2

We move all terms to the left:

65^2-(33^2+x^2)=0

We add all the numbers together, and all the variables

-(33^2+x^2)+4225=0

We get rid of parentheses

-x^2+4225-33^2=0

We add all the numbers together, and all the variables

-1x^2+3136=0

a = -1; b = 0; c = +3136;
Δ = b2-4ac
Δ = 02-4·(-1)·3136
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-112}{2*-1}=\frac{-112}{-2}
=+56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+112}{2*-1}=\frac{112}{-2}
=-56
$