450=0.4t^2+10t+50

Solution for 450=0.4t^2+10t+50 equation:

450=0.4t^2+10t+50

We move all terms to the left:

450-(0.4t^2+10t+50)=0

We get rid of parentheses

-0.4t^2-10t-50+450=0

We add all the numbers together, and all the variables

-0.4t^2-10t+400=0

a = -0.4; b = -10; c = +400;
Δ = b2-4ac
Δ = -102-4·(-0.4)·400
Δ = 740
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:

$\sqrt{\Delta}=\sqrt{740}=\sqrt{4*185}=\sqrt{4}*\sqrt{185}=2\sqrt{185}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{185}}{2*-0.4}=\frac{10-2\sqrt{185}}{-0.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{185}}{2*-0.4}=\frac{10+2\sqrt{185}}{-0.8}
$