3+30t-5t^2=13

Solution for 3+30t-5t^2=13 equation:

3+30t-5t^2=13

We move all terms to the left:

3+30t-5t^2-(13)=0

We add all the numbers together, and all the variables

-5t^2+30t-10=0

a = -5; b = 30; c = -10;
Δ = b2-4ac
Δ = 302-4·(-5)·(-10)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{7}}{2*-5}=\frac{-30-10\sqrt{7}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{7}}{2*-5}=\frac{-30+10\sqrt{7}}{-10}
$