(5x-40)(3x-2)=0

Solution for (5x-40)(3x-2)=0 equation:

(5x-40)(3x-2)=0

We multiply parentheses ..

(+15x^2-10x-120x+80)=0

We get rid of parentheses

15x^2-10x-120x+80=0

We add all the numbers together, and all the variables

15x^2-130x+80=0

a = 15; b = -130; c = +80;
Δ = b2-4ac
Δ = -1302-4·15·80
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-110}{2*15}=\frac{20}{30}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+110}{2*15}=\frac{240}{30}
=8
$