75=-12.6t+5t^2

Solution for 75=-12.6t+5t^2 equation:

75=-12.6t+5t^2

We move all terms to the left:

75-(-12.6t+5t^2)=0

We get rid of parentheses

-5t^2+12.6t+75=0

a = -5; b = 12.6; c = +75;
Δ = b2-4ac
Δ = 12.62-4·(-5)·75
Δ = 1658.76
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{-(12.6)-\sqrt{1658.76}}{2*-5}=\frac{-12.6-\sqrt{1658.76}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12.6)+\sqrt{1658.76}}{2*-5}=\frac{-12.6+\sqrt{1658.76}}{-10}
$