0=2x^2-7x-21

Solution for 0=2x^2-7x-21 equation:

0=2x^2-7x-21

We move all terms to the left:

0-(2x^2-7x-21)=0

We add all the numbers together, and all the variables

-(2x^2-7x-21)=0

We get rid of parentheses

-2x^2+7x+21=0

a = -2; b = 7; c = +21;
Δ = b2-4ac
Δ = 72-4·(-2)·21
Δ = 217
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{-(7)-\sqrt{217}}{2*-2}=\frac{-7-\sqrt{217}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{217}}{2*-2}=\frac{-7+\sqrt{217}}{-4}
$