(12x+1)(x-1)=-3

Solution for (12x+1)(x-1)=-3 equation:

(12x+1)(x-1)=-3

We move all terms to the left:

(12x+1)(x-1)-(-3)=0

We add all the numbers together, and all the variables

(12x+1)(x-1)+3=0

We multiply parentheses ..

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

We get rid of parentheses

12x^2-12x+x-1+3=0

We add all the numbers together, and all the variables

12x^2-11x+2=0

a = 12; b = -11; c = +2;
Δ = b2-4ac
Δ = -112-4·12·2
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5}{2*12}=\frac{6}{24}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*12}=\frac{16}{24}
=2/3
$