1000=(.0089(t^2))+1.1149t+78.4491

Solution for 1000=(.0089(t^2))+1.1149t+78.4491 equation:

1000=(.0089(t^2))+1.1149t+78.4491

We move all terms to the left:

1000-((.0089(t^2))+1.1149t+78.4491)=0


We calculate terms in parentheses: -((.0089t^2)+1.1149t+78.4491), so:

(.0089t^2)+1.1149t+78.4491

We add all the numbers together, and all the variables

1.1149t+(.0089t^2)+78.4491

We get rid of parentheses

.0089t^2+1.1149t+78.4491

Back to the equation:

-(.0089t^2+1.1149t+78.4491)


We get rid of parentheses

-.0089t^2-1.1149t-78.4491+1000=0

We add all the numbers together, and all the variables

-0.0089t^2-1.1149t+921.5509=0

a = -0.0089; b = -1.1149; c = +921.5509;
Δ = b2-4ac
Δ = -1.11492-4·(-0.0089)·921.5509
Δ = 34.05021405
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{-(-1.1149)-\sqrt{34.05021405}}{2*-0.0089}=\frac{1.1149-\sqrt{34.05021405}}{-0.0178}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.1149)+\sqrt{34.05021405}}{2*-0.0089}=\frac{1.1149+\sqrt{34.05021405}}{-0.0178}
$