50-15y-y^2=0

Solution for 50-15y-y^2=0 equation:

50-15y-y^2=0

We add all the numbers together, and all the variables

-1y^2-15y+50=0

a = -1; b = -15; c = +50;
Δ = b2-4ac
Δ = -152-4·(-1)·50
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{17}}{2*-1}=\frac{15-5\sqrt{17}}{-2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{17}}{2*-1}=\frac{15+5\sqrt{17}}{-2}
$