X(11-2x)=8

Solution for X(11-2x)=8 equation:

X(11-2X)=8

We move all terms to the left:

X(11-2X)-(8)=0

We add all the numbers together, and all the variables

X(-2X+11)-8=0

We multiply parentheses

-2X^2+11X-8=0

a = -2; b = 11; c = -8;
Δ = b2-4ac
Δ = 112-4·(-2)·(-8)
Δ = 57
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{-(11)-\sqrt{57}}{2*-2}=\frac{-11-\sqrt{57}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{57}}{2*-2}=\frac{-11+\sqrt{57}}{-4}
$