(2x+1)(x-1)=16x-8

Solution for (2x+1)(x-1)=16x-8 equation:

(2x+1)(x-1)=16x-8

We move all terms to the left:

(2x+1)(x-1)-(16x-8)=0

We get rid of parentheses

(2x+1)(x-1)-16x+8=0

We multiply parentheses ..

(+2x^2-2x+x-1)-16x+8=0

We get rid of parentheses

2x^2-2x+x-16x-1+8=0

We add all the numbers together, and all the variables

2x^2-17x+7=0

a = 2; b = -17; c = +7;
Δ = b2-4ac
Δ = -172-4·2·7
Δ = 233
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{-(-17)-\sqrt{233}}{2*2}=\frac{17-\sqrt{233}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{233}}{2*2}=\frac{17+\sqrt{233}}{4}
$