(4x-6)(x-2)=0

Solution for (4x-6)(x-2)=0 equation:

(4x-6)(x-2)=0

We multiply parentheses ..

(+4x^2-8x-6x+12)=0

We get rid of parentheses

4x^2-8x-6x+12=0

We add all the numbers together, and all the variables

4x^2-14x+12=0

a = 4; b = -14; c = +12;
Δ = b2-4ac
Δ = -142-4·4·12
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{-(-14)-2}{2*4}=\frac{12}{8}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2}{2*4}=\frac{16}{8}
=2
$