3/x+5/6x=4

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

3/x+5/6x=4

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


18x/6x^2+5x/6x^2-4=0

We multiply all the terms by the denominator


18x+5x-4*6x^2=0

We add all the numbers together, and all the variables

23x-4*6x^2=0

Wy multiply elements

-24x^2+23x=0

a = -24; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-24)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-24}=\frac{-46}{-48}
=23/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-24}=\frac{0}{-48}
=0
$