2w^2-15w+19=2w

Solution for 2w^2-15w+19=2w equation:

2w^2-15w+19=2w

We move all terms to the left:

2w^2-15w+19-(2w)=0

We add all the numbers together, and all the variables

2w^2-17w+19=0

a = 2; b = -17; c = +19;
Δ = b2-4ac
Δ = -172-4·2·19
Δ = 137
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{-(-17)-\sqrt{137}}{2*2}=\frac{17-\sqrt{137}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{137}}{2*2}=\frac{17+\sqrt{137}}{4}
$