5(3-4y)y=2

Solution for 5(3-4y)y=2 equation:

5(3-4y)y=2

We move all terms to the left:

5(3-4y)y-(2)=0

We add all the numbers together, and all the variables

5(-4y+3)y-2=0

We multiply parentheses

-20y^2+15y-2=0

a = -20; b = 15; c = -2;
Δ = b2-4ac
Δ = 152-4·(-20)·(-2)
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{65}}{2*-20}=\frac{-15-\sqrt{65}}{-40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{65}}{2*-20}=\frac{-15+\sqrt{65}}{-40}
$