3/4w+5=1/2w+9

Solution for 3/4w+5=1/2w+9 equation:

3/4w+5=1/2w+9

We move all terms to the left:

3/4w+5-(1/2w+9)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 2w+9)!=0

w∈R


We get rid of parentheses

3/4w-1/2w-9+5=0

We calculate fractions


6w/8w^2+(-4w)/8w^2-9+5=0

We add all the numbers together, and all the variables

6w/8w^2+(-4w)/8w^2-4=0

We multiply all the terms by the denominator


6w+(-4w)-4*8w^2=0

Wy multiply elements

-32w^2+6w+(-4w)=0

We get rid of parentheses

-32w^2+6w-4w=0

We add all the numbers together, and all the variables

-32w^2+2w=0

a = -32; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-32)·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*-32}=\frac{-4}{-64}
=1/16
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-32}=\frac{0}{-64}
=0
$