5y^2-14y+2=0

Solution for 5y^2-14y+2=0 equation:

5y^2-14y+2=0

a = 5; b = -14; c = +2;
Δ = b2-4ac
Δ = -142-4·5·2
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{39}}{2*5}=\frac{14-2\sqrt{39}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{39}}{2*5}=\frac{14+2\sqrt{39}}{10}
$