1/x=-7/3x+9

Solution for 1/x=-7/3x+9 equation:

1/x=-7/3x+9

We move all terms to the left:

1/x-(-7/3x+9)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

1/x+7/3x-9=0

We calculate fractions


3x/3x^2+7x/3x^2-9=0

We multiply all the terms by the denominator


3x+7x-9*3x^2=0

We add all the numbers together, and all the variables

10x-9*3x^2=0

Wy multiply elements

-27x^2+10x=0

a = -27; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-27)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-27}=\frac{-20}{-54}
=10/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-27}=\frac{0}{-54}
=0
$