5(2x-1)(3x+2)=0

Solution for 5(2x-1)(3x+2)=0 equation:

5(2x-1)(3x+2)=0

We multiply parentheses ..

5(+6x^2+4x-3x-2)=0

We multiply parentheses

30x^2+20x-15x-10=0

We add all the numbers together, and all the variables

30x^2+5x-10=0

a = 30; b = 5; c = -10;
Δ = b2-4ac
Δ = 52-4·30·(-10)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-35}{2*30}=\frac{-40}{60}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+35}{2*30}=\frac{30}{60}
=1/2
$