x(13-x)+x(8-x)=8

Solution for x(13-x)+x(8-x)=8 equation:

x(13-x)+x(8-x)=8

We move all terms to the left:

x(13-x)+x(8-x)-(8)=0

We add all the numbers together, and all the variables

x(-1x+13)+x(-1x+8)-8=0

We multiply parentheses

-1x^2-1x^2+13x+8x-8=0

We add all the numbers together, and all the variables

-2x^2+21x-8=0

a = -2; b = 21; c = -8;
Δ = b2-4ac
Δ = 212-4·(-2)·(-8)
Δ = 377
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{-(21)-\sqrt{377}}{2*-2}=\frac{-21-\sqrt{377}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{377}}{2*-2}=\frac{-21+\sqrt{377}}{-4}
$