8-x(5-x)=20

Solution for 8-x(5-x)=20 equation:

8-x(5-x)=20

We move all terms to the left:

8-x(5-x)-(20)=0

We add all the numbers together, and all the variables

-x(-1x+5)+8-20=0

We add all the numbers together, and all the variables

-x(-1x+5)-12=0

We multiply parentheses

1x^2-5x-12=0

We add all the numbers together, and all the variables

x^2-5x-12=0

a = 1; b = -5; c = -12;
Δ = b2-4ac
Δ = -52-4·1·(-12)
Δ = 73
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{-(-5)-\sqrt{73}}{2*1}=\frac{5-\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*1}=\frac{5+\sqrt{73}}{2}
$