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

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

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

We multiply parentheses ..

(+6x^2-24x-10x+40)=0

We get rid of parentheses

6x^2-24x-10x+40=0

We add all the numbers together, and all the variables

6x^2-34x+40=0

a = 6; b = -34; c = +40;
Δ = b2-4ac
Δ = -342-4·6·40
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-14}{2*6}=\frac{20}{12}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+14}{2*6}=\frac{48}{12}
=4
$