75=10t+5t^2

Solution for 75=10t+5t^2 equation:

75=10t+5t^2

We move all terms to the left:

75-(10t+5t^2)=0

We get rid of parentheses

-5t^2-10t+75=0

a = -5; b = -10; c = +75;
Δ = b2-4ac
Δ = -102-4·(-5)·75
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-40}{2*-5}=\frac{-30}{-10}
=+3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+40}{2*-5}=\frac{50}{-10}
=-5
$