-2w+44=3/4w

Solution for -2w+44=3/4w equation:

-2w+44=3/4w

We move all terms to the left:

-2w+44-(3/4w)=0


Domain of the equation: 4w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

-2w-(+3/4w)+44=0

We get rid of parentheses

-2w-3/4w+44=0

We multiply all the terms by the denominator


-2w*4w+44*4w-3=0

Wy multiply elements

-8w^2+176w-3=0

a = -8; b = 176; c = -3;
Δ = b2-4ac
Δ = 1762-4·(-8)·(-3)
Δ = 30880
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:

$\sqrt{\Delta}=\sqrt{30880}=\sqrt{16*1930}=\sqrt{16}*\sqrt{1930}=4\sqrt{1930}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(176)-4\sqrt{1930}}{2*-8}=\frac{-176-4\sqrt{1930}}{-16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(176)+4\sqrt{1930}}{2*-8}=\frac{-176+4\sqrt{1930}}{-16}
$