5(8u+9)u=8

Solution for 5(8u+9)u=8 equation:

5(8u+9)u=8

We move all terms to the left:

5(8u+9)u-(8)=0

We multiply parentheses

40u^2+45u-8=0

a = 40; b = 45; c = -8;
Δ = b2-4ac
Δ = 452-4·40·(-8)
Δ = 3305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{3305}}{2*40}=\frac{-45-\sqrt{3305}}{80}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{3305}}{2*40}=\frac{-45+\sqrt{3305}}{80}
$