3a^2=17+2a

Solution for 3a^2=17+2a equation:

3a^2=17+2a

We move all terms to the left:

3a^2-(17+2a)=0

We add all the numbers together, and all the variables

3a^2-(2a+17)=0

We get rid of parentheses

3a^2-2a-17=0

a = 3; b = -2; c = -17;
Δ = b2-4ac
Δ = -22-4·3·(-17)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{13}}{2*3}=\frac{2-4\sqrt{13}}{6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{13}}{2*3}=\frac{2+4\sqrt{13}}{6}
$