(8x-6)(3x-2)=0

Solution for (8x-6)(3x-2)=0 equation:

(8x-6)(3x-2)=0

We multiply parentheses ..

(+24x^2-16x-18x+12)=0

We get rid of parentheses

24x^2-16x-18x+12=0

We add all the numbers together, and all the variables

24x^2-34x+12=0

a = 24; b = -34; c = +12;
Δ = b2-4ac
Δ = -342-4·24·12
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2}{2*24}=\frac{32}{48}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2}{2*24}=\frac{36}{48}
=3/4
$