(x)=3x^2-6+1

Solution for (x)=3x^2-6+1 equation:

(x)=3x^2-6+1

We move all terms to the left:

(x)-(3x^2-6+1)=0

We get rid of parentheses

-3x^2+x+6-1=0

We add all the numbers together, and all the variables

-3x^2+x+5=0

a = -3; b = 1; c = +5;
Δ = b2-4ac
Δ = 12-4·(-3)·5
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{61}}{2*-3}=\frac{-1-\sqrt{61}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{61}}{2*-3}=\frac{-1+\sqrt{61}}{-6}
$