5x^2+12^2=39^2

Solution for 5x^2+12^2=39^2 equation:

5x^2+12^2=39^2

We move all terms to the left:

5x^2+12^2-(39^2)=0

We add all the numbers together, and all the variables

5x^2-1377=0

a = 5; b = 0; c = -1377;
Δ = b2-4ac
Δ = 02-4·5·(-1377)
Δ = 27540
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:

$\sqrt{\Delta}=\sqrt{27540}=\sqrt{324*85}=\sqrt{324}*\sqrt{85}=18\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{85}}{2*5}=\frac{0-18\sqrt{85}}{10}
=-\frac{18\sqrt{85}}{10}
=-\frac{9\sqrt{85}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{85}}{2*5}=\frac{0+18\sqrt{85}}{10}
=\frac{18\sqrt{85}}{10}
=\frac{9\sqrt{85}}{5}
$