1/7a+283=a

Solution for 1/7a+283=a equation:

1/7a+283=a

We move all terms to the left:

1/7a+283-(a)=0


Domain of the equation: 7a!=0

a!=0/7

a!=0

a∈R


We add all the numbers together, and all the variables

-1a+1/7a+283=0

We multiply all the terms by the denominator


-1a*7a+283*7a+1=0

Wy multiply elements

-7a^2+1981a+1=0

a = -7; b = 1981; c = +1;
Δ = b2-4ac
Δ = 19812-4·(-7)·1
Δ = 3924389
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1981)-\sqrt{3924389}}{2*-7}=\frac{-1981-\sqrt{3924389}}{-14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1981)+\sqrt{3924389}}{2*-7}=\frac{-1981+\sqrt{3924389}}{-14}
$