87/a=a

Solution for 87/a=a equation:

87/a=a

We move all terms to the left:

87/a-(a)=0


Domain of the equation: a!=0

a∈R


We add all the numbers together, and all the variables

-1a+87/a=0

We multiply all the terms by the denominator


-1a*a+87=0

Wy multiply elements

-1a^2+87=0

a = -1; b = 0; c = +87;
Δ = b2-4ac
Δ = 02-4·(-1)·87
Δ = 348
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:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{87}}{2*-1}=\frac{0-2\sqrt{87}}{-2}
=-\frac{2\sqrt{87}}{-2}
=-\frac{\sqrt{87}}{-1}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{87}}{2*-1}=\frac{0+2\sqrt{87}}{-2}
=\frac{2\sqrt{87}}{-2}
=\frac{\sqrt{87}}{-1}
$