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