9/4x+1/2x=44

Solution for 9/4x+1/2x=44 equation:

9/4x+1/2x=44

We move all terms to the left:

9/4x+1/2x-(44)=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 calculate fractions


18x/8x^2+4x/8x^2-44=0

We multiply all the terms by the denominator


18x+4x-44*8x^2=0

We add all the numbers together, and all the variables

22x-44*8x^2=0

Wy multiply elements

-352x^2+22x=0

a = -352; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·(-352)·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*-352}=\frac{-44}{-704}
=1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*-352}=\frac{0}{-704}
=0
$