115=23t+t^2

Solution for 115=23t+t^2 equation:

115=23t+t^2

We move all terms to the left:

115-(23t+t^2)=0

We get rid of parentheses

-t^2-23t+115=0

We add all the numbers together, and all the variables

-1t^2-23t+115=0

a = -1; b = -23; c = +115;
Δ = b2-4ac
Δ = -232-4·(-1)·115
Δ = 989
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{989}}{2*-1}=\frac{23-\sqrt{989}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{989}}{2*-1}=\frac{23+\sqrt{989}}{-2}
$