2/3x-1/2=1/5x+2

Solution for 2/3x-1/2=1/5x+2 equation:

2/3x-1/2=1/5x+2

We move all terms to the left:

2/3x-1/2-(1/5x+2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x+2)!=0

x∈R


We get rid of parentheses

2/3x-1/5x-2-1/2=0

We calculate fractions


(-75x^2)/60x^2+40x/60x^2+(-12x)/60x^2-2=0

We multiply all the terms by the denominator


(-75x^2)+40x+(-12x)-2*60x^2=0

Wy multiply elements

(-75x^2)-120x^2+40x+(-12x)=0

We get rid of parentheses

-75x^2-120x^2+40x-12x=0

We add all the numbers together, and all the variables

-195x^2+28x=0

a = -195; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-195)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-195}=\frac{-56}{-390}
=28/195
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-195}=\frac{0}{-390}
=0
$