2x(6x-4)=-3(x-1)

Solution for 2x(6x-4)=-3(x-1) equation:

2x(6x-4)=-3(x-1)

We move all terms to the left:

2x(6x-4)-(-3(x-1))=0

We multiply parentheses

12x^2-8x-(-3(x-1))=0


We calculate terms in parentheses: -(-3(x-1)), so:

-3(x-1)

We multiply parentheses

-3x+3

Back to the equation:

-(-3x+3)


We get rid of parentheses

12x^2-8x+3x-3=0

We add all the numbers together, and all the variables

12x^2-5x-3=0

a = 12; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·12·(-3)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*12}=\frac{-8}{24}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*12}=\frac{18}{24}
=3/4
$