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

Solution for (4x+1)(2x-7)=x equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+8x^2-28x+2x-7)-1x=0

We get rid of parentheses

8x^2-28x+2x-1x-7=0

We add all the numbers together, and all the variables

8x^2-27x-7=0

a = 8; b = -27; c = -7;
Δ = b2-4ac
Δ = -272-4·8·(-7)
Δ = 953
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{-(-27)-\sqrt{953}}{2*8}=\frac{27-\sqrt{953}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{953}}{2*8}=\frac{27+\sqrt{953}}{16}
$