-t^2+90t=1000

Solution for -t^2+90t=1000 equation:

-t^2+90t=1000

We move all terms to the left:

-t^2+90t-(1000)=0

We add all the numbers together, and all the variables

-1t^2+90t-1000=0

a = -1; b = 90; c = -1000;
Δ = b2-4ac
Δ = 902-4·(-1)·(-1000)
Δ = 4100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4100}=\sqrt{100*41}=\sqrt{100}*\sqrt{41}=10\sqrt{41}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-10\sqrt{41}}{2*-1}=\frac{-90-10\sqrt{41}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+10\sqrt{41}}{2*-1}=\frac{-90+10\sqrt{41}}{-2}
$