1/2a+15=a

Solution for 1/2a+15=a equation:

1/2a+15=a

We move all terms to the left:

1/2a+15-(a)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

-1a+1/2a+15=0

We multiply all the terms by the denominator


-1a*2a+15*2a+1=0

Wy multiply elements

-2a^2+30a+1=0

a = -2; b = 30; c = +1;
Δ = b2-4ac
Δ = 302-4·(-2)·1
Δ = 908
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:

$\sqrt{\Delta}=\sqrt{908}=\sqrt{4*227}=\sqrt{4}*\sqrt{227}=2\sqrt{227}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{227}}{2*-2}=\frac{-30-2\sqrt{227}}{-4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{227}}{2*-2}=\frac{-30+2\sqrt{227}}{-4}
$