(2x+1)(4x-1)=12x-3

Solution for (2x+1)(4x-1)=12x-3 equation:

(2x+1)(4x-1)=12x-3

We move all terms to the left:

(2x+1)(4x-1)-(12x-3)=0

We get rid of parentheses

(2x+1)(4x-1)-12x+3=0

We multiply parentheses ..

(+8x^2-2x+4x-1)-12x+3=0

We get rid of parentheses

8x^2-2x+4x-12x-1+3=0

We add all the numbers together, and all the variables

8x^2-10x+2=0

a = 8; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·8·2
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6}{2*8}=\frac{4}{16}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6}{2*8}=\frac{16}{16}
=1
$