(X-1)(40-x)=124

Solution for (X-1)(40-x)=124 equation:

(X-1)(40-X)=124

We move all terms to the left:

(X-1)(40-X)-(124)=0

We add all the numbers together, and all the variables

(X-1)(-1X+40)-124=0

We multiply parentheses ..

(-1X^2+40X+X-40)-124=0

We get rid of parentheses

-1X^2+40X+X-40-124=0

We add all the numbers together, and all the variables

-1X^2+41X-164=0

a = -1; b = 41; c = -164;
Δ = b2-4ac
Δ = 412-4·(-1)·(-164)
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-5\sqrt{41}}{2*-1}=\frac{-41-5\sqrt{41}}{-2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+5\sqrt{41}}{2*-1}=\frac{-41+5\sqrt{41}}{-2}
$