(x-5)(40-x)=4

Solution for (x-5)(40-x)=4 equation:

(x-5)(40-x)=4

We move all terms to the left:

(x-5)(40-x)-(4)=0

We add all the numbers together, and all the variables

(x-5)(-1x+40)-4=0

We multiply parentheses ..

(-1x^2+40x+5x-200)-4=0

We get rid of parentheses

-1x^2+40x+5x-200-4=0

We add all the numbers together, and all the variables

-1x^2+45x-204=0

a = -1; b = 45; c = -204;
Δ = b2-4ac
Δ = 452-4·(-1)·(-204)
Δ = 1209
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{1209}}{2*-1}=\frac{-45-\sqrt{1209}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{1209}}{2*-1}=\frac{-45+\sqrt{1209}}{-2}
$