-2/10x+9=3/5x-9

Solution for -2/10x+9=3/5x-9 equation:

-2/10x+9=3/5x-9

We move all terms to the left:

-2/10x+9-(3/5x-9)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x-9)!=0

x∈R


We get rid of parentheses

-2/10x-3/5x+9+9=0

We calculate fractions


(-10x)/50x^2+(-30x)/50x^2+9+9=0

We add all the numbers together, and all the variables

(-10x)/50x^2+(-30x)/50x^2+18=0

We multiply all the terms by the denominator


(-10x)+(-30x)+18*50x^2=0

Wy multiply elements

900x^2+(-10x)+(-30x)=0

We get rid of parentheses

900x^2-10x-30x=0

We add all the numbers together, and all the variables

900x^2-40x=0

a = 900; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·900·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*900}=\frac{0}{1800}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*900}=\frac{80}{1800}
=2/45
$