3(x+5)(2x-3)=0

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

3(x+5)(2x-3)=0

We multiply parentheses ..

3(+2x^2-3x+10x-15)=0

We multiply parentheses

6x^2-9x+30x-45=0

We add all the numbers together, and all the variables

6x^2+21x-45=0

a = 6; b = 21; c = -45;
Δ = b2-4ac
Δ = 212-4·6·(-45)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-39}{2*6}=\frac{-60}{12}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+39}{2*6}=\frac{18}{12}
=1+1/2
$