X=10/x-30

Solution for X=10/x-30 equation:

X=10/X-30

We move all terms to the left:

X-(10/X-30)=0


Domain of the equation: X-30)!=0

X∈R


We get rid of parentheses

X-10/X+30=0

We multiply all the terms by the denominator


X*X+30*X-10=0

We add all the numbers together, and all the variables

30X+X*X-10=0

Wy multiply elements

X^2+30X-10=0

a = 1; b = 30; c = -10;
Δ = b2-4ac
Δ = 302-4·1·(-10)
Δ = 940
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:

$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{235}}{2*1}=\frac{-30-2\sqrt{235}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{235}}{2*1}=\frac{-30+2\sqrt{235}}{2}
$