a+1/2a=99

Solution for a+1/2a=99 equation:

a+1/2a=99

We move all terms to the left:

a+1/2a-(99)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We multiply all the terms by the denominator


a*2a-99*2a+1=0

Wy multiply elements

2a^2-198a+1=0

a = 2; b = -198; c = +1;
Δ = b2-4ac
Δ = -1982-4·2·1
Δ = 39196
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:

$\sqrt{\Delta}=\sqrt{39196}=\sqrt{4*9799}=\sqrt{4}*\sqrt{9799}=2\sqrt{9799}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-198)-2\sqrt{9799}}{2*2}=\frac{198-2\sqrt{9799}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-198)+2\sqrt{9799}}{2*2}=\frac{198+2\sqrt{9799}}{4}
$