(3x-8)(5x+10)=0

Solution for (3x-8)(5x+10)=0 equation:

(3x-8)(5x+10)=0

We multiply parentheses ..

(+15x^2+30x-40x-80)=0

We get rid of parentheses

15x^2+30x-40x-80=0

We add all the numbers together, and all the variables

15x^2-10x-80=0

a = 15; b = -10; c = -80;
Δ = b2-4ac
Δ = -102-4·15·(-80)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-70}{2*15}=\frac{-60}{30}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+70}{2*15}=\frac{80}{30}
=2+2/3
$