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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


12x/20x^2+(-5x)/20x^2-1-6=0

We add all the numbers together, and all the variables

12x/20x^2+(-5x)/20x^2-7=0

We multiply all the terms by the denominator


12x+(-5x)-7*20x^2=0

Wy multiply elements

-140x^2+12x+(-5x)=0

We get rid of parentheses

-140x^2+12x-5x=0

We add all the numbers together, and all the variables

-140x^2+7x=0

a = -140; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-140)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-140}=\frac{-14}{-280}
=1/20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-140}=\frac{0}{-280}
=0
$