0=2x^2-14x-7

Solution for 0=2x^2-14x-7 equation:

0=2x^2-14x-7

We move all terms to the left:

0-(2x^2-14x-7)=0

We add all the numbers together, and all the variables

-(2x^2-14x-7)=0

We get rid of parentheses

-2x^2+14x+7=0

a = -2; b = 14; c = +7;
Δ = b2-4ac
Δ = 142-4·(-2)·7
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{7}}{2*-2}=\frac{-14-6\sqrt{7}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{7}}{2*-2}=\frac{-14+6\sqrt{7}}{-4}
$