1/2w+w=36

Solution for 1/2w+w=36 equation:

1/2w+w=36

We move all terms to the left:

1/2w+w-(36)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We add all the numbers together, and all the variables

w+1/2w-36=0

We multiply all the terms by the denominator


w*2w-36*2w+1=0

Wy multiply elements

2w^2-72w+1=0

a = 2; b = -72; c = +1;
Δ = b2-4ac
Δ = -722-4·2·1
Δ = 5176
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:

$\sqrt{\Delta}=\sqrt{5176}=\sqrt{4*1294}=\sqrt{4}*\sqrt{1294}=2\sqrt{1294}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1294}}{2*2}=\frac{72-2\sqrt{1294}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1294}}{2*2}=\frac{72+2\sqrt{1294}}{4}
$