X=9/y-4

Solution for X=9/y-4 equation:

X=9/X-4

We move all terms to the left:

X-(9/X-4)=0


Domain of the equation: X-4)!=0

X∈R


We get rid of parentheses

X-9/X+4=0

We multiply all the terms by the denominator


X*X+4*X-9=0

We add all the numbers together, and all the variables

4X+X*X-9=0

Wy multiply elements

X^2+4X-9=0

a = 1; b = 4; c = -9;
Δ = b2-4ac
Δ = 42-4·1·(-9)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{13}}{2*1}=\frac{-4-2\sqrt{13}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{13}}{2*1}=\frac{-4+2\sqrt{13}}{2}
$