-2t(8t-45)=0

Solution for -2t(8t-45)=0 equation:

-2t(8t-45)=0

We multiply parentheses

-16t^2+90t=0

a = -16; b = 90; c = 0;
Δ = b2-4ac
Δ = 902-4·(-16)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-90}{2*-16}=\frac{-180}{-32}
=5+5/8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+90}{2*-16}=\frac{0}{-32}
=0
$