3x^2=-8x+1

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

3x^2=-8x+1

We move all terms to the left:

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

We get rid of parentheses

3x^2+8x-1=0

a = 3; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·3·(-1)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{19}}{2*3}=\frac{-8-2\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{19}}{2*3}=\frac{-8+2\sqrt{19}}{6}
$