(x-5)(x-40)=124

Solution for (x-5)(x-40)=124 equation:

(x-5)(x-40)=124

We move all terms to the left:

(x-5)(x-40)-(124)=0

We multiply parentheses ..

(+x^2-40x-5x+200)-124=0

We get rid of parentheses

x^2-40x-5x+200-124=0

We add all the numbers together, and all the variables

x^2-45x+76=0

a = 1; b = -45; c = +76;
Δ = b2-4ac
Δ = -452-4·1·76
Δ = 1721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{1721}}{2*1}=\frac{45-\sqrt{1721}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1721}}{2*1}=\frac{45+\sqrt{1721}}{2}
$