X-9/3=56/x+4

Solution for X-9/3=56/x+4 equation:

X-9/3=56/X+4

We move all terms to the left:

X-9/3-(56/X+4)=0


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

X∈R


We add all the numbers together, and all the variables

X-(56/X+4)-3=0

We get rid of parentheses

X-56/X-4-3=0

We multiply all the terms by the denominator


X*X-4*X-3*X-56=0

We add all the numbers together, and all the variables

-7X+X*X-56=0

Wy multiply elements

X^2-7X-56=0

a = 1; b = -7; c = -56;
Δ = b2-4ac
Δ = -72-4·1·(-56)
Δ = 273
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{273}}{2*1}=\frac{7-\sqrt{273}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{273}}{2*1}=\frac{7+\sqrt{273}}{2}
$