-9u(u-2)=6u-27

Solution for -9u(u-2)=6u-27 equation:

-9u(u-2)=6u-27

We move all terms to the left:

-9u(u-2)-(6u-27)=0

We multiply parentheses

-9u^2+18u-(6u-27)=0

We get rid of parentheses

-9u^2+18u-6u+27=0

We add all the numbers together, and all the variables

-9u^2+12u+27=0

a = -9; b = 12; c = +27;
Δ = b2-4ac
Δ = 122-4·(-9)·27
Δ = 1116
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:

$\sqrt{\Delta}=\sqrt{1116}=\sqrt{36*31}=\sqrt{36}*\sqrt{31}=6\sqrt{31}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{31}}{2*-9}=\frac{-12-6\sqrt{31}}{-18}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{31}}{2*-9}=\frac{-12+6\sqrt{31}}{-18}
$