15=2w^2-w

Solution for 15=2w^2-w equation:

15=2w^2-w

We move all terms to the left:

15-(2w^2-w)=0

We get rid of parentheses

-2w^2+w+15=0

a = -2; b = 1; c = +15;
Δ = b2-4ac
Δ = 12-4·(-2)·15
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*-2}=\frac{-12}{-4}
=+3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*-2}=\frac{10}{-4}
=-2+1/2
$