5/4x+1/2x=44

Solution for 5/4x+1/2x=44 equation:

5/4x+1/2x=44

We move all terms to the left:

5/4x+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


10x/8x^2+4x/8x^2-44=0

We multiply all the terms by the denominator


10x+4x-44*8x^2=0

We add all the numbers together, and all the variables

14x-44*8x^2=0

Wy multiply elements

-352x^2+14x=0

a = -352; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-352)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-352}=\frac{-28}{-704}
=7/176
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-352}=\frac{0}{-704}
=0
$