4/3a=a+6

Solution for 4/3a=a+6 equation:

4/3a=a+6

We move all terms to the left:

4/3a-(a+6)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We get rid of parentheses

4/3a-a-6=0

We multiply all the terms by the denominator


-a*3a-6*3a+4=0

Wy multiply elements

-3a^2-18a+4=0

a = -3; b = -18; c = +4;
Δ = b2-4ac
Δ = -182-4·(-3)·4
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{93}}{2*-3}=\frac{18-2\sqrt{93}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{93}}{2*-3}=\frac{18+2\sqrt{93}}{-6}
$