a+38=11/2a

Solution for a+38=11/2a equation:

a+38=11/2a

We move all terms to the left:

a+38-(11/2a)=0


Domain of the equation: 2a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

a-(+11/2a)+38=0

We get rid of parentheses

a-11/2a+38=0

We multiply all the terms by the denominator


a*2a+38*2a-11=0

Wy multiply elements

2a^2+76a-11=0

a = 2; b = 76; c = -11;
Δ = b2-4ac
Δ = 762-4·2·(-11)
Δ = 5864
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:

$\sqrt{\Delta}=\sqrt{5864}=\sqrt{4*1466}=\sqrt{4}*\sqrt{1466}=2\sqrt{1466}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(76)-2\sqrt{1466}}{2*2}=\frac{-76-2\sqrt{1466}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(76)+2\sqrt{1466}}{2*2}=\frac{-76+2\sqrt{1466}}{4}
$