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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-30x^2+2x+(-15x)=0

We get rid of parentheses

-30x^2+2x-15x=0

We add all the numbers together, and all the variables

-30x^2-13x=0

a = -30; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·(-30)·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*-30}=\frac{0}{-60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-30}=\frac{26}{-60}
=-13/30
$