-2=t(-5t+40)

Solution for -2=t(-5t+40) equation:

-2=t(-5t+40)

We move all terms to the left:

-2-(t(-5t+40))=0


We calculate terms in parentheses: -(t(-5t+40)), so:

t(-5t+40)

We multiply parentheses

-5t^2+40t

Back to the equation:

-(-5t^2+40t)


We get rid of parentheses

5t^2-40t-2=0

a = 5; b = -40; c = -2;
Δ = b2-4ac
Δ = -402-4·5·(-2)
Δ = 1640
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:

$\sqrt{\Delta}=\sqrt{1640}=\sqrt{4*410}=\sqrt{4}*\sqrt{410}=2\sqrt{410}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{410}}{2*5}=\frac{40-2\sqrt{410}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{410}}{2*5}=\frac{40+2\sqrt{410}}{10}
$