2x^2-14=-x

Solution for 2x^2-14=-x equation:

2x^2-14=-x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

2x^2+1x-14=0

We add all the numbers together, and all the variables

2x^2+x-14=0

a = 2; b = 1; c = -14;
Δ = b2-4ac
Δ = 12-4·2·(-14)
Δ = 113
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{113}}{2*2}=\frac{-1-\sqrt{113}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{113}}{2*2}=\frac{-1+\sqrt{113}}{4}
$