-5t^2+30+200=165

Solution for -5t^2+30+200=165 equation:

-5t^2+30+200=165

We move all terms to the left:

-5t^2+30+200-(165)=0

We add all the numbers together, and all the variables

-5t^2+65=0

a = -5; b = 0; c = +65;
Δ = b2-4ac
Δ = 02-4·(-5)·65
Δ = 1300
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:

$\sqrt{\Delta}=\sqrt{1300}=\sqrt{100*13}=\sqrt{100}*\sqrt{13}=10\sqrt{13}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{13}}{2*-5}=\frac{0-10\sqrt{13}}{-10}
=-\frac{10\sqrt{13}}{-10}
=-\frac{\sqrt{13}}{-1}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{13}}{2*-5}=\frac{0+10\sqrt{13}}{-10}
=\frac{10\sqrt{13}}{-10}
=\frac{\sqrt{13}}{-1}
$