1/2x+9/5=2/3x-3

Solution for 1/2x+9/5=2/3x-3 equation:

1/2x+9/5=2/3x-3

We move all terms to the left:

1/2x+9/5-(2/3x-3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-3)!=0

x∈R


We get rid of parentheses

1/2x-2/3x+3+9/5=0

We calculate fractions


162x^2/150x^2+75x/150x^2+(-100x)/150x^2+3=0

We multiply all the terms by the denominator


162x^2+75x+(-100x)+3*150x^2=0

Wy multiply elements

162x^2+450x^2+75x+(-100x)=0

We get rid of parentheses

162x^2+450x^2+75x-100x=0

We add all the numbers together, and all the variables

612x^2-25x=0

a = 612; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·612·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*612}=\frac{0}{1224}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*612}=\frac{50}{1224}
=25/612
$