30=6/(a+a^2)

Solution for 30=6/(a+a^2) equation:

30=6/(a+a^2)

We move all terms to the left:

30-(6/(a+a^2))=0


Domain of the equation: (a+a^2))!=0

a∈R


We multiply all the terms by the denominator


-(6+30*(a+a^2))=0


We calculate terms in parentheses: -(6+30*(a+a^2)), so:

6+30*(a+a^2)

determiningTheFunctionDomain
30*(a+a^2)+6

We multiply parentheses

30a^2+30a+6

Back to the equation:

-(30a^2+30a+6)


We get rid of parentheses

-30a^2-30a-6=0

a = -30; b = -30; c = -6;
Δ = b2-4ac
Δ = -302-4·(-30)·(-6)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{5}}{2*-30}=\frac{30-6\sqrt{5}}{-60}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{5}}{2*-30}=\frac{30+6\sqrt{5}}{-60}
$