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

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

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

We multiply parentheses ..

5(+6x^2+9x-4x-6)=0

We multiply parentheses

30x^2+45x-20x-30=0

We add all the numbers together, and all the variables

30x^2+25x-30=0

a = 30; b = 25; c = -30;
Δ = b2-4ac
Δ = 252-4·30·(-30)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-65}{2*30}=\frac{-90}{60}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+65}{2*30}=\frac{40}{60}
=2/3
$