100(t)=0.81(t)^2

Solution for 100(t)=0.81(t)^2 equation:

100(t)=0.81(t)^2

We move all terms to the left:

100(t)-(0.81(t)^2)=0

We get rid of parentheses

-0.81t^2+100t=0

a = -0.81; b = 100; c = 0;
Δ = b2-4ac
Δ = 1002-4·(-0.81)·0
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100}{2*-0.81}=\frac{-200}{-1.62}
=123+0.73999999999998/1.62
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100}{2*-0.81}=\frac{0}{-1.62}
=0
$