11/4x+1/2x=-3

Solution for 11/4x+1/2x=-3 equation:

11/4x+1/2x=-3

We move all terms to the left:

11/4x+1/2x-(-3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

11/4x+1/2x+3=0

We calculate fractions


22x/8x^2+4x/8x^2+3=0

We multiply all the terms by the denominator


22x+4x+3*8x^2=0

We add all the numbers together, and all the variables

26x+3*8x^2=0

Wy multiply elements

24x^2+26x=0

a = 24; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·24·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*24}=\frac{-52}{48}
=-1+1/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*24}=\frac{0}{48}
=0
$