-10t*t+120t+200=0

Solution for -10t*t+120t+200=0 equation:

-10t*t+120t+200=0

We add all the numbers together, and all the variables

120t-10t*t+200=0

Wy multiply elements

-10t^2+120t+200=0

a = -10; b = 120; c = +200;
Δ = b2-4ac
Δ = 1202-4·(-10)·200
Δ = 22400
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:

$\sqrt{\Delta}=\sqrt{22400}=\sqrt{1600*14}=\sqrt{1600}*\sqrt{14}=40\sqrt{14}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-40\sqrt{14}}{2*-10}=\frac{-120-40\sqrt{14}}{-20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+40\sqrt{14}}{2*-10}=\frac{-120+40\sqrt{14}}{-20}
$