100/a=a+6

Solution for 100/a=a+6 equation:

100/a=a+6

We move all terms to the left:

100/a-(a+6)=0


Domain of the equation: a!=0

a∈R


We get rid of parentheses

100/a-a-6=0

We multiply all the terms by the denominator


-a*a-6*a+100=0

We add all the numbers together, and all the variables

-6a-a*a+100=0

Wy multiply elements

-1a^2-6a+100=0

a = -1; b = -6; c = +100;
Δ = b2-4ac
Δ = -62-4·(-1)·100
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{109}}{2*-1}=\frac{6-2\sqrt{109}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{109}}{2*-1}=\frac{6+2\sqrt{109}}{-2}
$