4/5a=a+6

Solution for 4/5a=a+6 equation:

4/5a=a+6

We move all terms to the left:

4/5a-(a+6)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We get rid of parentheses

4/5a-a-6=0

We multiply all the terms by the denominator


-a*5a-6*5a+4=0

Wy multiply elements

-5a^2-30a+4=0

a = -5; b = -30; c = +4;
Δ = b2-4ac
Δ = -302-4·(-5)·4
Δ = 980
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:

$\sqrt{\Delta}=\sqrt{980}=\sqrt{196*5}=\sqrt{196}*\sqrt{5}=14\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-14\sqrt{5}}{2*-5}=\frac{30-14\sqrt{5}}{-10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+14\sqrt{5}}{2*-5}=\frac{30+14\sqrt{5}}{-10}
$