1/5x-11/10=3/4x

Solution for 1/5x-11/10=3/4x equation:

1/5x-11/10=3/4x

We move all terms to the left:

1/5x-11/10-(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)-11/10=0

We get rid of parentheses

1/5x-3/4x-11/10=0

We calculate fractions


(-880x^2)/200x^2+40x/200x^2+(-150x)/200x^2=0

We multiply all the terms by the denominator


(-880x^2)+40x+(-150x)=0

We get rid of parentheses

-880x^2+40x-150x=0

We add all the numbers together, and all the variables

-880x^2-110x=0

a = -880; b = -110; c = 0;
Δ = b2-4ac
Δ = -1102-4·(-880)·0
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-110}{2*-880}=\frac{0}{-1760}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+110}{2*-880}=\frac{220}{-1760}
=-1/8
$