3/4w-44=-2w

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

3/4w-44=-2w

We move all terms to the left:

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


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We get rid of parentheses

3/4w+2w-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}
$