.5+w=8-3/2w

Solution for .5+w=8-3/2w equation:

.5+w=8-3/2w

We move all terms to the left:

.5+w-(8-3/2w)=0


Domain of the equation: 2w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

w-(-3/2w+8)+.5=0

We add all the numbers together, and all the variables

w-(-3/2w+8)+0.5=0

We get rid of parentheses

w+3/2w-8+0.5=0

We multiply all the terms by the denominator


w*2w-8*2w+(0.5)*2w+3=0

We multiply parentheses

w*2w-8*2w+w+3=0

Wy multiply elements

2w^2-16w+w+3=0

We add all the numbers together, and all the variables

2w^2-15w+3=0

a = 2; b = -15; c = +3;
Δ = b2-4ac
Δ = -152-4·2·3
Δ = 201
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{-(-15)-\sqrt{201}}{2*2}=\frac{15-\sqrt{201}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{201}}{2*2}=\frac{15+\sqrt{201}}{4}
$