3x(4x-3)=8x-6

Solution for 3x(4x-3)=8x-6 equation:

3x(4x-3)=8x-6

We move all terms to the left:

3x(4x-3)-(8x-6)=0

We multiply parentheses

12x^2-9x-(8x-6)=0

We get rid of parentheses

12x^2-9x-8x+6=0

We add all the numbers together, and all the variables

12x^2-17x+6=0

a = 12; b = -17; c = +6;
Δ = b2-4ac
Δ = -172-4·12·6
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-1}{2*12}=\frac{16}{24}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+1}{2*12}=\frac{18}{24}
=3/4
$