5y(3y-1)-3(2y)=7

Solution for 5y(3y-1)-3(2y)=7 equation:

5y(3y-1)-3(2y)=7

We move all terms to the left:

5y(3y-1)-3(2y)-(7)=0

We add all the numbers together, and all the variables

-32y+5y(3y-1)-7=0

We multiply parentheses

15y^2-32y-5y-7=0

We add all the numbers together, and all the variables

15y^2-37y-7=0

a = 15; b = -37; c = -7;
Δ = b2-4ac
Δ = -372-4·15·(-7)
Δ = 1789
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{-(-37)-\sqrt{1789}}{2*15}=\frac{37-\sqrt{1789}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{1789}}{2*15}=\frac{37+\sqrt{1789}}{30}
$