(2x+1)(x+2)=14

Solution for (2x+1)(x+2)=14 equation:

(2x+1)(x+2)=14

We move all terms to the left:

(2x+1)(x+2)-(14)=0

We multiply parentheses ..

(+2x^2+4x+x+2)-14=0

We get rid of parentheses

2x^2+4x+x+2-14=0

We add all the numbers together, and all the variables

2x^2+5x-12=0

a = 2; b = 5; c = -12;
Δ = b2-4ac
Δ = 52-4·2·(-12)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*2}=\frac{6}{4}
=1+1/2
$