3+1/a=17-3*a

Solution for 3+1/a=17-3*a equation:

3+1/a=17-3a

We move all terms to the left:

3+1/a-(17-3a)=0


Domain of the equation: a!=0

a∈R


We add all the numbers together, and all the variables

1/a-(-3a+17)+3=0

We get rid of parentheses

1/a+3a-17+3=0

We multiply all the terms by the denominator


3a*a-17*a+3*a+1=0

We add all the numbers together, and all the variables

-14a+3a*a+1=0

Wy multiply elements

3a^2-14a+1=0

a = 3; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·3·1
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{46}}{2*3}=\frac{14-2\sqrt{46}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{46}}{2*3}=\frac{14+2\sqrt{46}}{6}
$