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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


24x/18x^2+3x/18x^2-5=0

We multiply all the terms by the denominator


24x+3x-5*18x^2=0

We add all the numbers together, and all the variables

27x-5*18x^2=0

Wy multiply elements

-90x^2+27x=0

a = -90; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-90)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-90}=\frac{-54}{-180}
=3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-90}=\frac{0}{-180}
=0
$