34^2=18^2+x^2

Solution for 34^2=18^2+x^2 equation:

34^2=18^2+x^2

We move all terms to the left:

34^2-(18^2+x^2)=0

We add all the numbers together, and all the variables

-(18^2+x^2)+1156=0

We get rid of parentheses

-x^2+1156-18^2=0

We add all the numbers together, and all the variables

-1x^2+832=0

a = -1; b = 0; c = +832;
Δ = b2-4ac
Δ = 02-4·(-1)·832
Δ = 3328
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:

$\sqrt{\Delta}=\sqrt{3328}=\sqrt{256*13}=\sqrt{256}*\sqrt{13}=16\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{13}}{2*-1}=\frac{0-16\sqrt{13}}{-2}
=-\frac{16\sqrt{13}}{-2}
=-\frac{8\sqrt{13}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{13}}{2*-1}=\frac{0+16\sqrt{13}}{-2}
=\frac{16\sqrt{13}}{-2}
=\frac{8\sqrt{13}}{-1}
$