1/2w+9=2w

Solution for 1/2w+9=2w equation:

1/2w+9=2w

We move all terms to the left:

1/2w+9-(2w)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We add all the numbers together, and all the variables

-2w+1/2w+9=0

We multiply all the terms by the denominator


-2w*2w+9*2w+1=0

Wy multiply elements

-4w^2+18w+1=0

a = -4; b = 18; c = +1;
Δ = b2-4ac
Δ = 182-4·(-4)·1
Δ = 340
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{85}}{2*-4}=\frac{-18-2\sqrt{85}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{85}}{2*-4}=\frac{-18+2\sqrt{85}}{-8}
$