x+4/2=3/x+9

Solution for x+4/2=3/x+9 equation:

x+4/2=3/x+9

We move all terms to the left:

x+4/2-(3/x+9)=0


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

x∈R


We add all the numbers together, and all the variables

x-(3/x+9)+2=0

We get rid of parentheses

x-3/x-9+2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-7x+x*x-3=0

Wy multiply elements

x^2-7x-3=0

a = 1; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·1·(-3)
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{61}}{2*1}=\frac{7-\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{61}}{2*1}=\frac{7+\sqrt{61}}{2}
$