(2x+3)(4x-7)=x

Solution for (2x+3)(4x-7)=x equation:

(2x+3)(4x-7)=x

We move all terms to the left:

(2x+3)(4x-7)-(x)=0

We add all the numbers together, and all the variables

-1x+(2x+3)(4x-7)=0

We multiply parentheses ..

(+8x^2-14x+12x-21)-1x=0

We get rid of parentheses

8x^2-14x+12x-1x-21=0

We add all the numbers together, and all the variables

8x^2-3x-21=0

a = 8; b = -3; c = -21;
Δ = b2-4ac
Δ = -32-4·8·(-21)
Δ = 681
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{-(-3)-\sqrt{681}}{2*8}=\frac{3-\sqrt{681}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{681}}{2*8}=\frac{3+\sqrt{681}}{16}
$