33/4w+11/2w=7

Solution for 33/4w+11/2w=7 equation:

33/4w+11/2w=7

We move all terms to the left:

33/4w+11/2w-(7)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We calculate fractions


66w/8w^2+44w/8w^2-7=0

We multiply all the terms by the denominator


66w+44w-7*8w^2=0

We add all the numbers together, and all the variables

110w-7*8w^2=0

Wy multiply elements

-56w^2+110w=0

a = -56; b = 110; c = 0;
Δ = b2-4ac
Δ = 1102-4·(-56)·0
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-110}{2*-56}=\frac{-220}{-112}
=1+27/28
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+110}{2*-56}=\frac{0}{-112}
=0
$