4/3x=5/6x-5

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

4/3x=5/6x-5

We move all terms to the left:

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

We calculate fractions


24x/18x^2+(-15x)/18x^2+5=0

We multiply all the terms by the denominator


24x+(-15x)+5*18x^2=0

Wy multiply elements

90x^2+24x+(-15x)=0

We get rid of parentheses

90x^2+24x-15x=0

We add all the numbers together, and all the variables

90x^2+9x=0

a = 90; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·90·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*90}=\frac{-18}{180}
=-1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*90}=\frac{0}{180}
=0
$