a-1/2a=18

Solution for a-1/2a=18 equation:

a-1/2a=18

We move all terms to the left:

a-1/2a-(18)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We multiply all the terms by the denominator


a*2a-18*2a-1=0

Wy multiply elements

2a^2-36a-1=0

a = 2; b = -36; c = -1;
Δ = b2-4ac
Δ = -362-4·2·(-1)
Δ = 1304
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:

$\sqrt{\Delta}=\sqrt{1304}=\sqrt{4*326}=\sqrt{4}*\sqrt{326}=2\sqrt{326}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{326}}{2*2}=\frac{36-2\sqrt{326}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{326}}{2*2}=\frac{36+2\sqrt{326}}{4}
$