/9x-2=x+38

Solution for /9x-2=x+38 equation:

/9x-2=x+38

We move all terms to the left:

/9x-2-(x+38)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We get rid of parentheses

/9x-x-38-2=0

We multiply all the terms by the denominator


-x*9x-38*9x-2*9x+=0

We add all the numbers together, and all the variables

-x*9x-38*9x-2*9x=0

Wy multiply elements

-9x^2-342x-18x=0

We add all the numbers together, and all the variables

-9x^2-360x=0

a = -9; b = -360; c = 0;
Δ = b2-4ac
Δ = -3602-4·(-9)·0
Δ = 129600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{129600}=360$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-360}{2*-9}=\frac{0}{-18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+360}{2*-9}=\frac{720}{-18}
=-40
$