2/3x+1/2=3/5x-6

Solution for 2/3x+1/2=3/5x-6 equation:

2/3x+1/2=3/5x-6

We move all terms to the left:

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

2/3x-3/5x+6+1/2=0

We calculate fractions


75x^2/60x^2+40x/60x^2+(-36x)/60x^2+6=0

We multiply all the terms by the denominator


75x^2+40x+(-36x)+6*60x^2=0

Wy multiply elements

75x^2+360x^2+40x+(-36x)=0

We get rid of parentheses

75x^2+360x^2+40x-36x=0

We add all the numbers together, and all the variables

435x^2+4x=0

a = 435; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·435·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*435}=\frac{-8}{870}
=-4/435
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*435}=\frac{0}{870}
=0
$