1/5x-1/4x=11

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

1/5x-1/4x=11

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


4x/20x^2+(-5x)/20x^2-11=0

We multiply all the terms by the denominator


4x+(-5x)-11*20x^2=0

Wy multiply elements

-220x^2+4x+(-5x)=0

We get rid of parentheses

-220x^2+4x-5x=0

We add all the numbers together, and all the variables

-220x^2-1x=0

a = -220; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-220)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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