2/2x-4-5/3x-6=3/5

Solution for 2/2x-4-5/3x-6=3/5 equation:

2/2x-4-5/3x-6=3/5

We move all terms to the left:

2/2x-4-5/3x-6-(3/5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/2x-5/3x-4-6-(+3/5)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

2/2x-5/3x-10-3/5=0

We calculate fractions


(-54x^2)/150x^2+150x/150x^2+(-250x)/150x^2-10=0

We multiply all the terms by the denominator


(-54x^2)+150x+(-250x)-10*150x^2=0

Wy multiply elements

(-54x^2)-1500x^2+150x+(-250x)=0

We get rid of parentheses

-54x^2-1500x^2+150x-250x=0

We add all the numbers together, and all the variables

-1554x^2-100x=0

a = -1554; b = -100; c = 0;
Δ = b2-4ac
Δ = -1002-4·(-1554)·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-100}{2*-1554}=\frac{0}{-3108}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+100}{2*-1554}=\frac{200}{-3108}
=-50/777
$