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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+8x^2-28x+6x-21)-1x=0

We get rid of parentheses

8x^2-28x+6x-1x-21=0

We add all the numbers together, and all the variables

8x^2-23x-21=0

a = 8; b = -23; c = -21;
Δ = b2-4ac
Δ = -232-4·8·(-21)
Δ = 1201
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{-(-23)-\sqrt{1201}}{2*8}=\frac{23-\sqrt{1201}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{1201}}{2*8}=\frac{23+\sqrt{1201}}{16}
$