3x2-196=217x

Solution for 3x2-196=217x equation:

3x^2-196=217x

We move all terms to the left:

3x^2-196-(217x)=0

a = 3; b = -217; c = -196;
Δ = b2-4ac
Δ = -2172-4·3·(-196)
Δ = 49441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{49441}=\sqrt{49*1009}=\sqrt{49}*\sqrt{1009}=7\sqrt{1009}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-217)-7\sqrt{1009}}{2*3}=\frac{217-7\sqrt{1009}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-217)+7\sqrt{1009}}{2*3}=\frac{217+7\sqrt{1009}}{6}
$