-1/5x+6=-3/4x-5

Solution for -1/5x+6=-3/4x-5 equation:

-1/5x+6=-3/4x-5

We move all terms to the left:

-1/5x+6-(-3/4x-5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x-5)!=0

x∈R


We get rid of parentheses

-1/5x+3/4x+5+6=0

We calculate fractions


(-4x)/20x^2+15x/20x^2+5+6=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We get rid of parentheses

220x^2+15x-4x=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{-22}{440}
=-1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*220}=\frac{0}{440}
=0
$