2/5x+9=-6/10x

Solution for 2/5x+9=-6/10x equation:

2/5x+9=-6/10x

We move all terms to the left:

2/5x+9-(-6/10x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

2/5x+6/10x+9=0

We calculate fractions


20x/50x^2+30x/50x^2+9=0

We multiply all the terms by the denominator


20x+30x+9*50x^2=0

We add all the numbers together, and all the variables

50x+9*50x^2=0

Wy multiply elements

450x^2+50x=0

a = 450; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·450·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-50}{2*450}=\frac{-100}{900}
=-1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*450}=\frac{0}{900}
=0
$