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

Solution for 3(4y-3)(2y+5)=0 equation:

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

We multiply parentheses ..

3(+8y^2+20y-6y-15)=0

We multiply parentheses

24y^2+60y-18y-45=0

We add all the numbers together, and all the variables

24y^2+42y-45=0

a = 24; b = 42; c = -45;
Δ = b2-4ac
Δ = 422-4·24·(-45)
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*24}=\frac{-120}{48}
=-2+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+78}{2*24}=\frac{36}{48}
=3/4
$