0=2x^2+x-7

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

0=2x^2+x-7

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-2x^2-x+7=0

We add all the numbers together, and all the variables

-2x^2-1x+7=0

a = -2; b = -1; c = +7;
Δ = b2-4ac
Δ = -12-4·(-2)·7
Δ = 57
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{57}}{2*-2}=\frac{1-\sqrt{57}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{57}}{2*-2}=\frac{1+\sqrt{57}}{-4}
$