2w^2-3w=17

Solution for 2w^2-3w=17 equation:

2w^2-3w=17

We move all terms to the left:

2w^2-3w-(17)=0

a = 2; b = -3; c = -17;
Δ = b2-4ac
Δ = -32-4·2·(-17)
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{145}}{2*2}=\frac{3-\sqrt{145}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{145}}{2*2}=\frac{3+\sqrt{145}}{4}
$