(15x-8)(x-5)=0

Solution for (15x-8)(x-5)=0 equation:

(15x-8)(x-5)=0

We multiply parentheses ..

(+15x^2-75x-8x+40)=0

We get rid of parentheses

15x^2-75x-8x+40=0

We add all the numbers together, and all the variables

15x^2-83x+40=0

a = 15; b = -83; c = +40;
Δ = b2-4ac
Δ = -832-4·15·40
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-83)-67}{2*15}=\frac{16}{30}
=8/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-83)+67}{2*15}=\frac{150}{30}
=5
$