2-3/4w=1/8w+9

Solution for 2-3/4w=1/8w+9 equation:

2-3/4w=1/8w+9

We move all terms to the left:

2-3/4w-(1/8w+9)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 8w+9)!=0

w∈R


We get rid of parentheses

-3/4w-1/8w-9+2=0

We calculate fractions


(-24w)/32w^2+(-4w)/32w^2-9+2=0

We add all the numbers together, and all the variables

(-24w)/32w^2+(-4w)/32w^2-7=0

We multiply all the terms by the denominator


(-24w)+(-4w)-7*32w^2=0

Wy multiply elements

-224w^2+(-24w)+(-4w)=0

We get rid of parentheses

-224w^2-24w-4w=0

We add all the numbers together, and all the variables

-224w^2-28w=0

a = -224; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·(-224)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*-224}=\frac{0}{-448}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*-224}=\frac{56}{-448}
=-1/8
$