6(u-2)8u=-30

Solution for 6(u-2)8u=-30 equation:

6(u-2)8u=-30

We move all terms to the left:

6(u-2)8u-(-30)=0

We add all the numbers together, and all the variables

6(u-2)8u+30=0

We multiply parentheses

48u^2-96u+30=0

a = 48; b = -96; c = +30;
Δ = b2-4ac
Δ = -962-4·48·30
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-24\sqrt{6}}{2*48}=\frac{96-24\sqrt{6}}{96}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+24\sqrt{6}}{2*48}=\frac{96+24\sqrt{6}}{96}
$