3x^2-2x+1=97

Solution for 3x^2-2x+1=97 equation:

3x^2-2x+1=97

We move all terms to the left:

3x^2-2x+1-(97)=0

We add all the numbers together, and all the variables

3x^2-2x-96=0

a = 3; b = -2; c = -96;
Δ = b2-4ac
Δ = -22-4·3·(-96)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-34}{2*3}=\frac{-32}{6}
=-5+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+34}{2*3}=\frac{36}{6}
=6
$