(1)/(4)w+(1)/(2)w+5=11

Solution for (1)/(4)w+(1)/(2)w+5=11 equation:

(1)/(4)w+(1)/(2)w+5=11

We move all terms to the left:

(1)/(4)w+(1)/(2)w+5-(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 add all the numbers together, and all the variables

1/4w+1/2w-6=0

We calculate fractions


2w/8w^2+4w/8w^2-6=0

We multiply all the terms by the denominator


2w+4w-6*8w^2=0

We add all the numbers together, and all the variables

6w-6*8w^2=0

Wy multiply elements

-48w^2+6w=0

a = -48; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-48)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-48}=\frac{-12}{-96}
=1/8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-48}=\frac{0}{-96}
=0
$