u^2=13-8u

Solution for u^2=13-8u equation:

u^2=13-8u

We move all terms to the left:

u^2-(13-8u)=0

We add all the numbers together, and all the variables

u^2-(-8u+13)=0

We get rid of parentheses

u^2+8u-13=0

a = 1; b = 8; c = -13;
Δ = b2-4ac
Δ = 82-4·1·(-13)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{29}}{2*1}=\frac{-8-2\sqrt{29}}{2}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{29}}{2*1}=\frac{-8+2\sqrt{29}}{2}
$