Y=-x^2-10X+21

Solution for Y=-x^2-10X+21 equation:

=-Y^2-10Y+21

We move all terms to the left:

-(-Y^2-10Y+21)=0

We get rid of parentheses

Y^2+10Y-21=0

a = 1; b = 10; c = -21;
Δ = b2-4ac
Δ = 102-4·1·(-21)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{46}}{2*1}=\frac{-10-2\sqrt{46}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{46}}{2*1}=\frac{-10+2\sqrt{46}}{2}
$