w-2=(19-2w)^(1/2)

Solution for w-2=(19-2w)^(1/2) equation:

w-2=(19-2w)^(1/2)

We move all terms to the left:

w-2-((19-2w)^(1/2))=0

We add all the numbers together, and all the variables

w-((-2w+19)^(+1/2))-2=0

We multiply all the terms by the denominator


w*2))-((-2w+1+19)^(-2*2))=0

We add all the numbers together, and all the variables

w*2))-((-2w+20)^(-4))=0

We add all the numbers together, and all the variables

-2w+w*2))-((=0

Wy multiply elements

2w^2-2w=0

a = 2; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·2·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*2}=\frac{0}{4}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*2}=\frac{4}{4}
=1
$