150=5t+t^2

Solution for 150=5t+t^2 equation:

150=5t+t^2

We move all terms to the left:

150-(5t+t^2)=0

We get rid of parentheses

-t^2-5t+150=0

We add all the numbers together, and all the variables

-1t^2-5t+150=0

a = -1; b = -5; c = +150;
Δ = b2-4ac
Δ = -52-4·(-1)·150
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-25}{2*-1}=\frac{-20}{-2}
=+10
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+25}{2*-1}=\frac{30}{-2}
=-15
$