(x+10)(x+5)=24

Solution for (x+10)(x+5)=24 equation:

(x+10)(x+5)=24

We move all terms to the left:

(x+10)(x+5)-(24)=0

We multiply parentheses ..

(+x^2+5x+10x+50)-24=0

We get rid of parentheses

x^2+5x+10x+50-24=0

We add all the numbers together, and all the variables

x^2+15x+26=0

a = 1; b = 15; c = +26;
Δ = b2-4ac
Δ = 152-4·1·26
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-11}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+11}{2*1}=\frac{-4}{2}
=-2
$