t(-4.5t+1.25)=0

Solution for t(-4.5t+1.25)=0 equation:

t(-4.5t+1.25)=0

We multiply parentheses

-4t^2+1.25t=0

a = -4; b = 1.25; c = 0;
Δ = b2-4ac
Δ = 1.252-4·(-4)·0
Δ = 1.5625
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{-(1.25)-\sqrt{1.5625}}{2*-4}=\frac{-1.25-\sqrt{1.5625}}{-8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.25)+\sqrt{1.5625}}{2*-4}=\frac{-1.25+\sqrt{1.5625}}{-8}
$