80=10t^2-40t-370

Solution for 80=10t^2-40t-370 equation:

80=10t^2-40t-370

We move all terms to the left:

80-(10t^2-40t-370)=0

We get rid of parentheses

-10t^2+40t+370+80=0

We add all the numbers together, and all the variables

-10t^2+40t+450=0

a = -10; b = 40; c = +450;
Δ = b2-4ac
Δ = 402-4·(-10)·450
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-140}{2*-10}=\frac{-180}{-20}
=+9
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+140}{2*-10}=\frac{100}{-20}
=-5
$