180=15t+7.5t^2

Solution for 180=15t+7.5t^2 equation:

180=15t+7.5t^2

We move all terms to the left:

180-(15t+7.5t^2)=0

We get rid of parentheses

-7.5t^2-15t+180=0

a = -7.5; b = -15; c = +180;
Δ = b2-4ac
Δ = -152-4·(-7.5)·180
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-75}{2*-7.5}=\frac{-60}{-15}
=+4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+75}{2*-7.5}=\frac{90}{-15}
=-6
$