(X+1)(2x-1)-6=0

Solution for (X+1)(2x-1)-6=0 equation:

(X+1)(2X-1)-6=0

We multiply parentheses ..

(+2X^2-1X+2X-1)-6=0

We get rid of parentheses

2X^2-1X+2X-1-6=0

We add all the numbers together, and all the variables

2X^2+X-7=0

a = 2; b = 1; c = -7;
Δ = b2-4ac
Δ = 12-4·2·(-7)
Δ = 57
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{-(1)-\sqrt{57}}{2*2}=\frac{-1-\sqrt{57}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{57}}{2*2}=\frac{-1+\sqrt{57}}{4}
$