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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+6x^2-6x-16x+16)=0

We get rid of parentheses

6x^2-6x-16x+16=0

We add all the numbers together, and all the variables

6x^2-22x+16=0

a = 6; b = -22; c = +16;
Δ = b2-4ac
Δ = -222-4·6·16
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-10}{2*6}=\frac{12}{12}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+10}{2*6}=\frac{32}{12}
=2+2/3
$