14x^2-46x+2=0

Solution for 14x^2-46x+2=0 equation:

14x^2-46x+2=0

a = 14; b = -46; c = +2;
Δ = b2-4ac
Δ = -462-4·14·2
Δ = 2004
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:

$\sqrt{\Delta}=\sqrt{2004}=\sqrt{4*501}=\sqrt{4}*\sqrt{501}=2\sqrt{501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{501}}{2*14}=\frac{46-2\sqrt{501}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{501}}{2*14}=\frac{46+2\sqrt{501}}{28}
$