(x-5)(45-x)=4

Solution for (x-5)(45-x)=4 equation:

(x-5)(45-x)=4

We move all terms to the left:

(x-5)(45-x)-(4)=0

We add all the numbers together, and all the variables

(x-5)(-1x+45)-4=0

We multiply parentheses ..

(-1x^2+45x+5x-225)-4=0

We get rid of parentheses

-1x^2+45x+5x-225-4=0

We add all the numbers together, and all the variables

-1x^2+50x-229=0

a = -1; b = 50; c = -229;
Δ = b2-4ac
Δ = 502-4·(-1)·(-229)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-12\sqrt{11}}{2*-1}=\frac{-50-12\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+12\sqrt{11}}{2*-1}=\frac{-50+12\sqrt{11}}{-2}
$