4/3x+10=4/5x+6

Solution for 4/3x+10=4/5x+6 equation:

4/3x+10=4/5x+6

We move all terms to the left:

4/3x+10-(4/5x+6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

4/3x-4/5x-6+10=0

We calculate fractions


20x/15x^2+(-12x)/15x^2-6+10=0

We add all the numbers together, and all the variables

20x/15x^2+(-12x)/15x^2+4=0

We multiply all the terms by the denominator


20x+(-12x)+4*15x^2=0

Wy multiply elements

60x^2+20x+(-12x)=0

We get rid of parentheses

60x^2+20x-12x=0

We add all the numbers together, and all the variables

60x^2+8x=0

a = 60; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·60·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*60}=\frac{-16}{120}
=-2/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*60}=\frac{0}{120}
=0
$