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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


576x^2/600x^2+450x/600x^2+100x/600x^2=0

We multiply all the terms by the denominator


576x^2+450x+100x=0

We add all the numbers together, and all the variables

576x^2+550x=0

a = 576; b = 550; c = 0;
Δ = b2-4ac
Δ = 5502-4·576·0
Δ = 302500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{302500}=550$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(550)-550}{2*576}=\frac{-1100}{1152}
=-275/288
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(550)+550}{2*576}=\frac{0}{1152}
=0
$