(2x+1)(x+1)=22

Solution for (2x+1)(x+1)=22 equation:

(2x+1)(x+1)=22

We move all terms to the left:

(2x+1)(x+1)-(22)=0

We multiply parentheses ..

(+2x^2+2x+x+1)-22=0

We get rid of parentheses

2x^2+2x+x+1-22=0

We add all the numbers together, and all the variables

2x^2+3x-21=0

a = 2; b = 3; c = -21;
Δ = b2-4ac
Δ = 32-4·2·(-21)
Δ = 177
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{-(3)-\sqrt{177}}{2*2}=\frac{-3-\sqrt{177}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{177}}{2*2}=\frac{-3+\sqrt{177}}{4}
$