X=6/y+4

Solution for X=6/y+4 equation:

X=6/X+4

We move all terms to the left:

X-(6/X+4)=0


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

X∈R


We get rid of parentheses

X-6/X-4=0

We multiply all the terms by the denominator


X*X-4*X-6=0

We add all the numbers together, and all the variables

-4X+X*X-6=0

Wy multiply elements

X^2-4X-6=0

a = 1; b = -4; c = -6;
Δ = b2-4ac
Δ = -42-4·1·(-6)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{10}}{2*1}=\frac{4-2\sqrt{10}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{10}}{2*1}=\frac{4+2\sqrt{10}}{2}
$