-1/5x+4=2/3x-1

Solution for -1/5x+4=2/3x-1 equation:

-1/5x+4=2/3x-1

We move all terms to the left:

-1/5x+4-(2/3x-1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

-1/5x-2/3x+1+4=0

We calculate fractions


(-3x)/15x^2+(-10x)/15x^2+1+4=0

We add all the numbers together, and all the variables

(-3x)/15x^2+(-10x)/15x^2+5=0

We multiply all the terms by the denominator


(-3x)+(-10x)+5*15x^2=0

Wy multiply elements

75x^2+(-3x)+(-10x)=0

We get rid of parentheses

75x^2-3x-10x=0

We add all the numbers together, and all the variables

75x^2-13x=0

a = 75; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·75·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*75}=\frac{0}{150}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*75}=\frac{26}{150}
=13/75
$