90=t+2.5t^2

Solution for 90=t+2.5t^2 equation:

90=t+2.5t^2

We move all terms to the left:

90-(t+2.5t^2)=0

We get rid of parentheses

-2.5t^2-t+90=0

We add all the numbers together, and all the variables

-2.5t^2-1t+90=0

a = -2.5; b = -1; c = +90;
Δ = b2-4ac
Δ = -12-4·(-2.5)·90
Δ = 901
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{901}}{2*-2.5}=\frac{1-\sqrt{901}}{-5}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{901}}{2*-2.5}=\frac{1+\sqrt{901}}{-5}
$