-2u(u-1)=8u-18

Solution for -2u(u-1)=8u-18 equation:

-2u(u-1)=8u-18

We move all terms to the left:

-2u(u-1)-(8u-18)=0

We multiply parentheses

-2u^2+2u-(8u-18)=0

We get rid of parentheses

-2u^2+2u-8u+18=0

We add all the numbers together, and all the variables

-2u^2-6u+18=0

a = -2; b = -6; c = +18;
Δ = b2-4ac
Δ = -62-4·(-2)·18
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{5}}{2*-2}=\frac{6-6\sqrt{5}}{-4}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{5}}{2*-2}=\frac{6+6\sqrt{5}}{-4}
$