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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

2x^2-1x+2x-1-4=0

We add all the numbers together, and all the variables

2x^2+x-5=0

a = 2; b = 1; c = -5;
Δ = b2-4ac
Δ = 12-4·2·(-5)
Δ = 41
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{41}}{2*2}=\frac{-1-\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{41}}{2*2}=\frac{-1+\sqrt{41}}{4}
$