u(8u-39)=5

Solution for u(8u-39)=5 equation:

u(8u-39)=5

We move all terms to the left:

u(8u-39)-(5)=0

We multiply parentheses

8u^2-39u-5=0

a = 8; b = -39; c = -5;
Δ = b2-4ac
Δ = -392-4·8·(-5)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-41}{2*8}=\frac{-2}{16}
=-1/8
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+41}{2*8}=\frac{80}{16}
=5
$