6(2y+3)(y-5)=0

Solution for 6(2y+3)(y-5)=0 equation:

6(2y+3)(y-5)=0

We multiply parentheses ..

6(+2y^2-10y+3y-15)=0

We multiply parentheses

12y^2-60y+18y-90=0

We add all the numbers together, and all the variables

12y^2-42y-90=0

a = 12; b = -42; c = -90;
Δ = b2-4ac
Δ = -422-4·12·(-90)
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-78}{2*12}=\frac{-36}{24}
=-1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+78}{2*12}=\frac{120}{24}
=5
$