(9)(10-5/9x)=(1/3x+2)(9)

Solution for (9)(10-5/9x)=(1/3x+2)(9) equation:

(9)(10-5/9x)=(1/3x+2)(9)

We move all terms to the left:

(9)(10-5/9x)-((1/3x+2)(9))=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3x+2)9)!=0

x∈R


We add all the numbers together, and all the variables

9(-5/9x+10)-((1/3x+2)9)=0

We multiply parentheses

-45x-((1/3x+2)9)+90=0

We multiply all the terms by the denominator


-45x*3x+90*3x+2)9)-((1+2)9)=0

We add all the numbers together, and all the variables

-45x*3x+90*3x+2)9)-(39)=0

We add all the numbers together, and all the variables

-45x*3x+90*3x=0

Wy multiply elements

-135x^2+270x=0

a = -135; b = 270; c = 0;
Δ = b2-4ac
Δ = 2702-4·(-135)·0
Δ = 72900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{72900}=270$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-270}{2*-135}=\frac{-540}{-270}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+270}{2*-135}=\frac{0}{-270}
=0
$