3x2-14x+1=0

Solution for 3x2-14x+1=0 equation:

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}
$