u^2=2u^2-18u+24

Solution for u^2=2u^2-18u+24 equation:

u^2=2u^2-18u+24

We move all terms to the left:

u^2-(2u^2-18u+24)=0

We get rid of parentheses

u^2-2u^2+18u-24=0

We add all the numbers together, and all the variables

-1u^2+18u-24=0

a = -1; b = 18; c = -24;
Δ = b2-4ac
Δ = 182-4·(-1)·(-24)
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{57}}{2*-1}=\frac{-18-2\sqrt{57}}{-2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{57}}{2*-1}=\frac{-18+2\sqrt{57}}{-2}
$