5*5-(x+5)(x+3)=0

Solution for 5*5-(x+5)(x+3)=0 equation:

5*5-(x+5)(x+3)=0

We add all the numbers together, and all the variables

-(x+5)(x+3)+25=0

We multiply parentheses ..

-(+x^2+3x+5x+15)+25=0

We get rid of parentheses

-x^2-3x-5x-15+25=0

We add all the numbers together, and all the variables

-1x^2-8x+10=0

a = -1; b = -8; c = +10;
Δ = b2-4ac
Δ = -82-4·(-1)·10
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{-(-8)-2\sqrt{26}}{2*-1}=\frac{8-2\sqrt{26}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{26}}{2*-1}=\frac{8+2\sqrt{26}}{-2}
$