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

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

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

We multiply parentheses ..

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

We multiply parentheses

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

We add all the numbers together, and all the variables

10x^2-5x-30=0

a = 10; b = -5; c = -30;
Δ = b2-4ac
Δ = -52-4·10·(-30)
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*10}=\frac{-30}{20}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+35}{2*10}=\frac{40}{20}
=2
$