(55-a+15)/a=a

Solution for (55-a+15)/a=a equation:

(55-a+15)/a=a

We move all terms to the left:

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


Domain of the equation: a!=0

a∈R


We add all the numbers together, and all the variables

(-1a+70)/a-a=0

We add all the numbers together, and all the variables

-1a+(-1a+70)/a=0

We multiply all the terms by the denominator


-1a*a+(-1a+70)=0

Wy multiply elements

-1a^2+(-1a+70)=0

We get rid of parentheses

-1a^2-1a+70=0

a = -1; b = -1; c = +70;
Δ = b2-4ac
Δ = -12-4·(-1)·70
Δ = 281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{281}}{2*-1}=\frac{1-\sqrt{281}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{281}}{2*-1}=\frac{1+\sqrt{281}}{-2}
$