t=-16t^2+10+15

Solution for t=-16t^2+10+15 equation:

t=-16t^2+10+15

We move all terms to the left:

t-(-16t^2+10+15)=0

We get rid of parentheses

16t^2+t-10-15=0

We add all the numbers together, and all the variables

16t^2+t-25=0

a = 16; b = 1; c = -25;
Δ = b2-4ac
Δ = 12-4·16·(-25)
Δ = 1601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{1601}}{2*16}=\frac{-1-\sqrt{1601}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1601}}{2*16}=\frac{-1+\sqrt{1601}}{32}
$