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

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

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

We multiply parentheses ..

5(+3x^2+x-15x-5)=0

We multiply parentheses

15x^2+5x-75x-25=0

We add all the numbers together, and all the variables

15x^2-70x-25=0

a = 15; b = -70; c = -25;
Δ = b2-4ac
Δ = -702-4·15·(-25)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-80}{2*15}=\frac{-10}{30}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+80}{2*15}=\frac{150}{30}
=5
$