2y^2-14y-7=0

Solution for 2y^2-14y-7=0 equation:

2y^2-14y-7=0

a = 2; b = -14; c = -7;
Δ = b2-4ac
Δ = -142-4·2·(-7)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{7}}{2*2}=\frac{14-6\sqrt{7}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{7}}{2*2}=\frac{14+6\sqrt{7}}{4}
$