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

Solution for 8(x)=3x^2-6x+1 equation:

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

We move all terms to the left:

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

We get rid of parentheses

-3x^2+8x+6x-1=0

We add all the numbers together, and all the variables

-3x^2+14x-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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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