11/4x+5=11/2x

Solution for 11/4x+5=11/2x equation:

11/4x+5=11/2x

We move all terms to the left:

11/4x+5-(11/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

11/4x-(+11/2x)+5=0

We get rid of parentheses

11/4x-11/2x+5=0

We calculate fractions


22x/8x^2+(-44x)/8x^2+5=0

We multiply all the terms by the denominator


22x+(-44x)+5*8x^2=0

Wy multiply elements

40x^2+22x+(-44x)=0

We get rid of parentheses

40x^2+22x-44x=0

We add all the numbers together, and all the variables

40x^2-22x=0

a = 40; b = -22; c = 0;
Δ = b2-4ac
Δ = -222-4·40·0
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*40}=\frac{0}{80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+22}{2*40}=\frac{44}{80}
=11/20
$