2w^2-17w+33=0

Solution for 2w^2-17w+33=0 equation:

2w^2-17w+33=0

a = 2; b = -17; c = +33;
Δ = b2-4ac
Δ = -172-4·2·33
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-5}{2*2}=\frac{12}{4}
=3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+5}{2*2}=\frac{22}{4}
=5+1/2
$