5(2q-1)3q=30

Solution for 5(2q-1)3q=30 equation:

5(2q-1)3q=30

We move all terms to the left:

5(2q-1)3q-(30)=0

We multiply parentheses

30q^2-15q-30=0

a = 30; b = -15; c = -30;
Δ = b2-4ac
Δ = -152-4·30·(-30)
Δ = 3825
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3825}=\sqrt{225*17}=\sqrt{225}*\sqrt{17}=15\sqrt{17}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15\sqrt{17}}{2*30}=\frac{15-15\sqrt{17}}{60}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15\sqrt{17}}{2*30}=\frac{15+15\sqrt{17}}{60}
$