2/5x-4=9/10x-9

Solution for 2/5x-4=9/10x-9 equation:

2/5x-4=9/10x-9

We move all terms to the left:

2/5x-4-(9/10x-9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x-9)!=0

x∈R


We get rid of parentheses

2/5x-9/10x+9-4=0

We calculate fractions


20x/50x^2+(-45x)/50x^2+9-4=0

We add all the numbers together, and all the variables

20x/50x^2+(-45x)/50x^2+5=0

We multiply all the terms by the denominator


20x+(-45x)+5*50x^2=0

Wy multiply elements

250x^2+20x+(-45x)=0

We get rid of parentheses

250x^2+20x-45x=0

We add all the numbers together, and all the variables

250x^2-25x=0

a = 250; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·250·0
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*250}=\frac{0}{500}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*250}=\frac{50}{500}
=1/10
$