(t*t)+400t-10,000=0

Solution for (t*t)+400t-10,000=0 equation:

(t*t)+400t-10.000=0

We add all the numbers together, and all the variables

(+t*t)+400t-10.000=0

We add all the numbers together, and all the variables

400t+(+t*t)-10=0

We get rid of parentheses

400t+t*t-10=0

Wy multiply elements

t^2+400t-10=0

a = 1; b = 400; c = -10;
Δ = b2-4ac
Δ = 4002-4·1·(-10)
Δ = 160040
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:

$\sqrt{\Delta}=\sqrt{160040}=\sqrt{4*40010}=\sqrt{4}*\sqrt{40010}=2\sqrt{40010}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(400)-2\sqrt{40010}}{2*1}=\frac{-400-2\sqrt{40010}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(400)+2\sqrt{40010}}{2*1}=\frac{-400+2\sqrt{40010}}{2}
$