6/x+4=12/5x-12

Solution for 6/x+4=12/5x-12 equation:

6/x+4=12/5x-12

We move all terms to the left:

6/x+4-(12/5x-12)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x-12)!=0

x∈R


We get rid of parentheses

6/x-12/5x+12+4=0

We calculate fractions


30x/5x^2+(-12x)/5x^2+12+4=0

We add all the numbers together, and all the variables

30x/5x^2+(-12x)/5x^2+16=0

We multiply all the terms by the denominator


30x+(-12x)+16*5x^2=0

Wy multiply elements

80x^2+30x+(-12x)=0

We get rid of parentheses

80x^2+30x-12x=0

We add all the numbers together, and all the variables

80x^2+18x=0

a = 80; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·80·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*80}=\frac{-36}{160}
=-9/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*80}=\frac{0}{160}
=0
$