1/5a+8=9a

Solution for 1/5a+8=9a equation:

1/5a+8=9a

We move all terms to the left:

1/5a+8-(9a)=0


Domain of the equation: 5a!=0

a!=0/5

a!=0

a∈R


We add all the numbers together, and all the variables

-9a+1/5a+8=0

We multiply all the terms by the denominator


-9a*5a+8*5a+1=0

Wy multiply elements

-45a^2+40a+1=0

a = -45; b = 40; c = +1;
Δ = b2-4ac
Δ = 402-4·(-45)·1
Δ = 1780
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:

$\sqrt{\Delta}=\sqrt{1780}=\sqrt{4*445}=\sqrt{4}*\sqrt{445}=2\sqrt{445}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{445}}{2*-45}=\frac{-40-2\sqrt{445}}{-90}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{445}}{2*-45}=\frac{-40+2\sqrt{445}}{-90}
$