(x+5)2=(x)2-15

Solution for (x+5)2=(x)2-15 equation:

(x+5)2=(x)2-15

We move all terms to the left:

(x+5)2-((x)2-15)=0

We add all the numbers together, and all the variables

-(+x^2-15)+(x+5)2=0

We multiply parentheses

-(+x^2-15)+2x+10=0

We get rid of parentheses

-x^2+2x+15+10=0

We add all the numbers together, and all the variables

-1x^2+2x+25=0

a = -1; b = 2; c = +25;
Δ = b2-4ac
Δ = 22-4·(-1)·25
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{26}}{2*-1}=\frac{-2-2\sqrt{26}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{26}}{2*-1}=\frac{-2+2\sqrt{26}}{-2}
$