7^2+x^2=15^2

Solution for 7^2+x^2=15^2 equation:

7^2+x^2=15^2

We move all terms to the left:

7^2+x^2-(15^2)=0

We add all the numbers together, and all the variables

x^2-176=0

a = 1; b = 0; c = -176;
Δ = b2-4ac
Δ = 02-4·1·(-176)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{11}}{2*1}=\frac{0-8\sqrt{11}}{2}
=-\frac{8\sqrt{11}}{2}
=-4\sqrt{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{11}}{2*1}=\frac{0+8\sqrt{11}}{2}
=\frac{8\sqrt{11}}{2}
=4\sqrt{11}
$