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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


81x/135x^2+20x/135x^2+(-10x)/135x^2-4=0

We multiply all the terms by the denominator


81x+20x+(-10x)-4*135x^2=0

We add all the numbers together, and all the variables

101x+(-10x)-4*135x^2=0

Wy multiply elements

-540x^2+101x+(-10x)=0

We get rid of parentheses

-540x^2+101x-10x=0

We add all the numbers together, and all the variables

-540x^2+91x=0

a = -540; b = 91; c = 0;
Δ = b2-4ac
Δ = 912-4·(-540)·0
Δ = 8281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8281}=91$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(91)-91}{2*-540}=\frac{-182}{-1080}
=91/540
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+91}{2*-540}=\frac{0}{-1080}
=0
$