1/5x+11=3/4x

Solution for 1/5x+11=3/4x equation:

1/5x+11=3/4x

We move all terms to the left:

1/5x+11-(3/4x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(+3/4x)+11=0

We get rid of parentheses

1/5x-3/4x+11=0

We calculate fractions


4x/20x^2+(-15x)/20x^2+11=0

We multiply all the terms by the denominator


4x+(-15x)+11*20x^2=0

Wy multiply elements

220x^2+4x+(-15x)=0

We get rid of parentheses

220x^2+4x-15x=0

We add all the numbers together, and all the variables

220x^2-11x=0

a = 220; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·220·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*220}=\frac{0}{440}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*220}=\frac{22}{440}
=1/20
$