u^2-8u+16=2u^2-9u-4

Solution for u^2-8u+16=2u^2-9u-4 equation:

u^2-8u+16=2u^2-9u-4

We move all terms to the left:

u^2-8u+16-(2u^2-9u-4)=0

We get rid of parentheses

u^2-2u^2-8u+9u+4+16=0

We add all the numbers together, and all the variables

-1u^2+u+20=0

a = -1; b = 1; c = +20;
Δ = b2-4ac
Δ = 12-4·(-1)·20
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-9}{2*-1}=\frac{-10}{-2}
=+5
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+9}{2*-1}=\frac{8}{-2}
=-4
$