2a^2-a=14

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

2a^2-a=14

We move all terms to the left:

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

We add all the numbers together, and all the variables

2a^2-1a-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:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{113}}{2*2}=\frac{1-\sqrt{113}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{113}}{2*2}=\frac{1+\sqrt{113}}{4}
$