0=2w^2+5w-63

Solution for 0=2w^2+5w-63 equation:

0=2w^2+5w-63

We move all terms to the left:

0-(2w^2+5w-63)=0

We add all the numbers together, and all the variables

-(2w^2+5w-63)=0

We get rid of parentheses

-2w^2-5w+63=0

a = -2; b = -5; c = +63;
Δ = b2-4ac
Δ = -52-4·(-2)·63
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-23}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+23}{2*-2}=\frac{28}{-4}
=-7
$