15t+7.5t^2=180

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

15t+7.5t^2=180

We move all terms to the left:

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