-2y^2-14y+5=0

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

-2y^2-14y+5=0

a = -2; b = -14; c = +5;
Δ = b2-4ac
Δ = -142-4·(-2)·5
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{59}}{2*-2}=\frac{14-2\sqrt{59}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{59}}{2*-2}=\frac{14+2\sqrt{59}}{-4}
$