21/4x-1/2x=44

Solution for 21/4x-1/2x=44 equation:

21/4x-1/2x=44

We move all terms to the left:

21/4x-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


42x/8x^2+(-4x)/8x^2-44=0

We multiply all the terms by the denominator


42x+(-4x)-44*8x^2=0

Wy multiply elements

-352x^2+42x+(-4x)=0

We get rid of parentheses

-352x^2+42x-4x=0

We add all the numbers together, and all the variables

-352x^2+38x=0

a = -352; b = 38; c = 0;
Δ = b2-4ac
Δ = 382-4·(-352)·0
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-38}{2*-352}=\frac{-76}{-704}
=19/176
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+38}{2*-352}=\frac{0}{-704}
=0
$