9x+30=10/x

Solution for 9x+30=10/x equation:

9x+30=10/x

We move all terms to the left:

9x+30-(10/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9x-(+10/x)+30=0

We get rid of parentheses

9x-10/x+30=0

We multiply all the terms by the denominator


9x*x+30*x-10=0

We add all the numbers together, and all the variables

30x+9x*x-10=0

Wy multiply elements

9x^2+30x-10=0

a = 9; b = 30; c = -10;
Δ = b2-4ac
Δ = 302-4·9·(-10)
Δ = 1260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{35}}{2*9}=\frac{-30-6\sqrt{35}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{35}}{2*9}=\frac{-30+6\sqrt{35}}{18}
$