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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


45x^2/60x^2+24x/60x^2+(-20x)/60x^2+9=0

We multiply all the terms by the denominator


45x^2+24x+(-20x)+9*60x^2=0

Wy multiply elements

45x^2+540x^2+24x+(-20x)=0

We get rid of parentheses

45x^2+540x^2+24x-20x=0

We add all the numbers together, and all the variables

585x^2+4x=0

a = 585; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·585·0
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*585}=\frac{-8}{1170}
=-4/585
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*585}=\frac{0}{1170}
=0
$