(3/2)w+1=w+9/2

Solution for (3/2)w+1=w+9/2 equation:

(3/2)w+1=w+9/2

We move all terms to the left:

(3/2)w+1-(w+9/2)=0


Domain of the equation: 2)w!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

(+3/2)w-(+w+9/2)+1=0

We multiply parentheses

3w^2-(+w+9/2)+1=0

We get rid of parentheses

3w^2-w+1-9/2=0

We multiply all the terms by the denominator


3w^2*2-w*2-9+1*2=0

We add all the numbers together, and all the variables

3w^2*2-w*2-7=0

Wy multiply elements

6w^2-2w-7=0

a = 6; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·6·(-7)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{43}}{2*6}=\frac{2-2\sqrt{43}}{12}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{43}}{2*6}=\frac{2+2\sqrt{43}}{12}
$