-5t^2+15t+115=3t+3

Solution for -5t^2+15t+115=3t+3 equation:

-5t^2+15t+115=3t+3

We move all terms to the left:

-5t^2+15t+115-(3t+3)=0

We get rid of parentheses

-5t^2+15t-3t-3+115=0

We add all the numbers together, and all the variables

-5t^2+12t+112=0

a = -5; b = 12; c = +112;
Δ = b2-4ac
Δ = 122-4·(-5)·112
Δ = 2384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2384}=\sqrt{16*149}=\sqrt{16}*\sqrt{149}=4\sqrt{149}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{149}}{2*-5}=\frac{-12-4\sqrt{149}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{149}}{2*-5}=\frac{-12+4\sqrt{149}}{-10}
$