4/5a-8=a+2

Solution for 4/5a-8=a+2 equation:

4/5a-8=a+2

We move all terms to the left:

4/5a-8-(a+2)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We get rid of parentheses

4/5a-a-2-8=0

We multiply all the terms by the denominator


-a*5a-2*5a-8*5a+4=0

Wy multiply elements

-5a^2-10a-40a+4=0

We add all the numbers together, and all the variables

-5a^2-50a+4=0

a = -5; b = -50; c = +4;
Δ = b2-4ac
Δ = -502-4·(-5)·4
Δ = 2580
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:

$\sqrt{\Delta}=\sqrt{2580}=\sqrt{4*645}=\sqrt{4}*\sqrt{645}=2\sqrt{645}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{645}}{2*-5}=\frac{50-2\sqrt{645}}{-10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{645}}{2*-5}=\frac{50+2\sqrt{645}}{-10}
$