2w^2-9w+3=2w

Solution for 2w^2-9w+3=2w equation:

2w^2-9w+3=2w

We move all terms to the left:

2w^2-9w+3-(2w)=0

We add all the numbers together, and all the variables

2w^2-11w+3=0

a = 2; b = -11; c = +3;
Δ = b2-4ac
Δ = -112-4·2·3
Δ = 97
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{-(-11)-\sqrt{97}}{2*2}=\frac{11-\sqrt{97}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{97}}{2*2}=\frac{11+\sqrt{97}}{4}
$