8(3x-5)(x-2)=0

Solution for 8(3x-5)(x-2)=0 equation:

8(3x-5)(x-2)=0

We multiply parentheses ..

8(+3x^2-6x-5x+10)=0

We multiply parentheses

24x^2-48x-40x+80=0

We add all the numbers together, and all the variables

24x^2-88x+80=0

a = 24; b = -88; c = +80;
Δ = b2-4ac
Δ = -882-4·24·80
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-8}{2*24}=\frac{80}{48}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+8}{2*24}=\frac{96}{48}
=2
$