5(2x+1)(3x-4)=0

Solution for 5(2x+1)(3x-4)=0 equation:

5(2x+1)(3x-4)=0

We multiply parentheses ..

5(+6x^2-8x+3x-4)=0

We multiply parentheses

30x^2-40x+15x-20=0

We add all the numbers together, and all the variables

30x^2-25x-20=0

a = 30; b = -25; c = -20;
Δ = b2-4ac
Δ = -252-4·30·(-20)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-55}{2*30}=\frac{-30}{60}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+55}{2*30}=\frac{80}{60}
=1+1/3
$