Y=-t2+3t+10

Solution for Y=-t2+3t+10 equation:

=-Y2+3Y+10

We move all terms to the left:

-(-Y2+3Y+10)=0

We add all the numbers together, and all the variables

-(-1Y^2+3Y+10)=0

We get rid of parentheses

1Y^2-3Y-10=0

We add all the numbers together, and all the variables

Y^2-3Y-10=0

a = 1; b = -3; c = -10;
Δ = b2-4ac
Δ = -32-4·1·(-10)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*1}=\frac{-4}{2}
=-2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*1}=\frac{10}{2}
=5
$