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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+6x^2-2x-9x+3)-4=0

We get rid of parentheses

6x^2-2x-9x+3-4=0

We add all the numbers together, and all the variables

6x^2-11x-1=0

a = 6; b = -11; c = -1;
Δ = b2-4ac
Δ = -112-4·6·(-1)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-\sqrt{145}}{2*6}=\frac{11-\sqrt{145}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{145}}{2*6}=\frac{11+\sqrt{145}}{12}
$