3/4w+7-2w=-2

Solution for 3/4w+7-2w=-2 equation:

3/4w+7-2w=-2

We move all terms to the left:

3/4w+7-2w-(-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+9=0

We multiply all the terms by the denominator


-2w*4w+9*4w+3=0

Wy multiply elements

-8w^2+36w+3=0

a = -8; b = 36; c = +3;
Δ = b2-4ac
Δ = 362-4·(-8)·3
Δ = 1392
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:

$\sqrt{\Delta}=\sqrt{1392}=\sqrt{16*87}=\sqrt{16}*\sqrt{87}=4\sqrt{87}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-4\sqrt{87}}{2*-8}=\frac{-36-4\sqrt{87}}{-16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+4\sqrt{87}}{2*-8}=\frac{-36+4\sqrt{87}}{-16}
$