-y^2+14y-34=0

Solution for -y^2+14y-34=0 equation:

-y^2+14y-34=0

We add all the numbers together, and all the variables

-1y^2+14y-34=0

a = -1; b = 14; c = -34;
Δ = b2-4ac
Δ = 142-4·(-1)·(-34)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{15}}{2*-1}=\frac{-14-2\sqrt{15}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{15}}{2*-1}=\frac{-14+2\sqrt{15}}{-2}
$