41/4w+31/2w=11

Solution for 41/4w+31/2w=11 equation:

41/4w+31/2w=11

We move all terms to the left:

41/4w+31/2w-(11)=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


82w/8w^2+124w/8w^2-11=0

We multiply all the terms by the denominator


82w+124w-11*8w^2=0

We add all the numbers together, and all the variables

206w-11*8w^2=0

Wy multiply elements

-88w^2+206w=0

a = -88; b = 206; c = 0;
Δ = b2-4ac
Δ = 2062-4·(-88)·0
Δ = 42436
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{42436}=206$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(206)-206}{2*-88}=\frac{-412}{-176}
=2+15/44
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(206)+206}{2*-88}=\frac{0}{-176}
=0
$