75=10t+t^2

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

75=10t+t^2

We move all terms to the left:

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

We get rid of parentheses

-t^2-10t+75=0

We add all the numbers together, and all the variables

-1t^2-10t+75=0

a = -1; b = -10; c = +75;
Δ = b2-4ac
Δ = -102-4·(-1)·75
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20}{2*-1}=\frac{-10}{-2}
=+5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20}{2*-1}=\frac{30}{-2}
=-15
$