a+4/a=15/a-4

Solution for a+4/a=15/a-4 equation:

a+4/a=15/a-4

We move all terms to the left:

a+4/a-(15/a-4)=0


Domain of the equation: a!=0

a∈R



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

a∈R


We get rid of parentheses

a+4/a-15/a+4=0

We multiply all the terms by the denominator


a*a+4*a+4-15=0

We add all the numbers together, and all the variables

4a+a*a-11=0

Wy multiply elements

a^2+4a-11=0

a = 1; b = 4; c = -11;
Δ = b2-4ac
Δ = 42-4·1·(-11)
Δ = 60
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{15}}{2*1}=\frac{-4-2\sqrt{15}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{15}}{2*1}=\frac{-4+2\sqrt{15}}{2}
$