9t^2+30t+16=80

Solution for 9t^2+30t+16=80 equation:

9t^2+30t+16=80

We move all terms to the left:

9t^2+30t+16-(80)=0

We add all the numbers together, and all the variables

9t^2+30t-64=0

a = 9; b = 30; c = -64;
Δ = b2-4ac
Δ = 302-4·9·(-64)
Δ = 3204
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:

$\sqrt{\Delta}=\sqrt{3204}=\sqrt{36*89}=\sqrt{36}*\sqrt{89}=6\sqrt{89}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{89}}{2*9}=\frac{-30-6\sqrt{89}}{18}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{89}}{2*9}=\frac{-30+6\sqrt{89}}{18}
$