4/5x-3=2/3x+5

Solution for 4/5x-3=2/3x+5 equation:

4/5x-3=2/3x+5

We move all terms to the left:

4/5x-3-(2/3x+5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

4/5x-2/3x-5-3=0

We calculate fractions


12x/15x^2+(-10x)/15x^2-5-3=0

We add all the numbers together, and all the variables

12x/15x^2+(-10x)/15x^2-8=0

We multiply all the terms by the denominator


12x+(-10x)-8*15x^2=0

Wy multiply elements

-120x^2+12x+(-10x)=0

We get rid of parentheses

-120x^2+12x-10x=0

We add all the numbers together, and all the variables

-120x^2+2x=0

a = -120; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-120)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-120}=\frac{-4}{-240}
=1/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-120}=\frac{0}{-240}
=0
$