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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

8x^2-11x-3=0

a = 8; b = -11; c = -3;
Δ = b2-4ac
Δ = -112-4·8·(-3)
Δ = 217
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{217}}{2*8}=\frac{11-\sqrt{217}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{217}}{2*8}=\frac{11+\sqrt{217}}{16}
$