3(3x-4)(2x=1)

Solution for 3(3x-4)(2x=1) equation:

3(3x-4)(2x=1)

We move all terms to the left:

3(3x-4)(2x-(1))=0

We multiply parentheses ..

3(+6x^2-3x-8x+4)=0

We multiply parentheses

18x^2-9x-24x+12=0

We add all the numbers together, and all the variables

18x^2-33x+12=0

a = 18; b = -33; c = +12;
Δ = b2-4ac
Δ = -332-4·18·12
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-15}{2*18}=\frac{18}{36}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+15}{2*18}=\frac{48}{36}
=1+1/3
$