5(3y-1)3(2y)=10

Solution for 5(3y-1)3(2y)=10 equation:

5(3y-1)3(2y)=10

We move all terms to the left:

5(3y-1)3(2y)-(10)=0

We multiply parentheses

480y^2-160y-10=0

a = 480; b = -160; c = -10;
Δ = b2-4ac
Δ = -1602-4·480·(-10)
Δ = 44800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44800}=\sqrt{6400*7}=\sqrt{6400}*\sqrt{7}=80\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-80\sqrt{7}}{2*480}=\frac{160-80\sqrt{7}}{960}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+80\sqrt{7}}{2*480}=\frac{160+80\sqrt{7}}{960}
$