2(x+1)x=14

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

2(x+1)x=14

We move all terms to the left:

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

We multiply parentheses

2x^2+2x-14=0

a = 2; b = 2; c = -14;
Δ = b2-4ac
Δ = 22-4·2·(-14)
Δ = 116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{29}}{2*2}=\frac{-2-2\sqrt{29}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{29}}{2*2}=\frac{-2+2\sqrt{29}}{4}
$