3/4w+-2w=-2

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

3/4w+-2w=-2

We move all terms to the left:

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


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -8; b = 8; c = +3;
Δ = b2-4ac
Δ = 82-4·(-8)·3
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{10}}{2*-8}=\frac{-8-4\sqrt{10}}{-16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{10}}{2*-8}=\frac{-8+4\sqrt{10}}{-16}
$