2x^2+1=2x+14

Solution for 2x^2+1=2x+14 equation:

2x^2+1=2x+14

We move all terms to the left:

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

We get rid of parentheses

2x^2-2x-14+1=0

We add all the numbers together, and all the variables

2x^2-2x-13=0

a = 2; b = -2; c = -13;
Δ = b2-4ac
Δ = -22-4·2·(-13)
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{3}}{2*2}=\frac{2-6\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{3}}{2*2}=\frac{2+6\sqrt{3}}{4}
$