X+14=x+2x2

Solution for X+14=x+2x2 equation:

X+14=X+2X^2

We move all terms to the left:

X+14-(X+2X^2)=0

We get rid of parentheses

-2X^2-X+X+14=0

We add all the numbers together, and all the variables

-2X^2+14=0

a = -2; b = 0; c = +14;
Δ = b2-4ac
Δ = 02-4·(-2)·14
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*-2}=\frac{0-4\sqrt{7}}{-4}
=-\frac{4\sqrt{7}}{-4}
=-\frac{\sqrt{7}}{-1}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*-2}=\frac{0+4\sqrt{7}}{-4}
=\frac{4\sqrt{7}}{-4}
=\frac{\sqrt{7}}{-1}
$