1/9x=1/10x+4

Solution for 1/9x=1/10x+4 equation:

1/9x=1/10x+4

We move all terms to the left:

1/9x-(1/10x+4)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 10x+4)!=0

x∈R


We get rid of parentheses

1/9x-1/10x-4=0

We calculate fractions


10x/90x^2+(-9x)/90x^2-4=0

We multiply all the terms by the denominator


10x+(-9x)-4*90x^2=0

Wy multiply elements

-360x^2+10x+(-9x)=0

We get rid of parentheses

-360x^2+10x-9x=0

We add all the numbers together, and all the variables

-360x^2+x=0

a = -360; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-360)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-360}=\frac{-2}{-720}
=1/360
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-360}=\frac{0}{-720}
=0
$