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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x-6)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


12x/15x^2+(-25x)/15x^2+6+3=0

We add all the numbers together, and all the variables

12x/15x^2+(-25x)/15x^2+9=0

We multiply all the terms by the denominator


12x+(-25x)+9*15x^2=0

Wy multiply elements

135x^2+12x+(-25x)=0

We get rid of parentheses

135x^2+12x-25x=0

We add all the numbers together, and all the variables

135x^2-13x=0

a = 135; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·135·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*135}=\frac{0}{270}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*135}=\frac{26}{270}
=13/135
$