2y^2-14y+1=0

Solution for 2y^2-14y+1=0 equation:

2y^2-14y+1=0

a = 2; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·2·1
Δ = 188
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{47}}{2*2}=\frac{14-2\sqrt{47}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{47}}{2*2}=\frac{14+2\sqrt{47}}{4}
$