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

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

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

We multiply parentheses ..

5(+6x^2-8x+15x-20)=0

We multiply parentheses

30x^2-40x+75x-100=0

We add all the numbers together, and all the variables

30x^2+35x-100=0

a = 30; b = 35; c = -100;
Δ = b2-4ac
Δ = 352-4·30·(-100)
Δ = 13225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13225}=115$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-115}{2*30}=\frac{-150}{60}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+115}{2*30}=\frac{80}{60}
=1+1/3
$