0=2x^2-5x-14

Solution for 0=2x^2-5x-14 equation:

0=2x^2-5x-14

We move all terms to the left:

0-(2x^2-5x-14)=0

We add all the numbers together, and all the variables

-(2x^2-5x-14)=0

We get rid of parentheses

-2x^2+5x+14=0

a = -2; b = 5; c = +14;
Δ = b2-4ac
Δ = 52-4·(-2)·14
Δ = 137
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{-(5)-\sqrt{137}}{2*-2}=\frac{-5-\sqrt{137}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{137}}{2*-2}=\frac{-5+\sqrt{137}}{-4}
$