Y=-x^2+13x-34

Solution for Y=-x^2+13x-34 equation:

=-Y^2+13Y-34

We move all terms to the left:

-(-Y^2+13Y-34)=0

We get rid of parentheses

Y^2-13Y+34=0

a = 1; b = -13; c = +34;
Δ = b2-4ac
Δ = -132-4·1·34
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{33}}{2*1}=\frac{13-\sqrt{33}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{33}}{2*1}=\frac{13+\sqrt{33}}{2}
$