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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8x^2-10x-3=0

a = 8; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·8·(-3)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14}{2*8}=\frac{-4}{16}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*8}=\frac{24}{16}
=1+1/2
$