40,000=134t+8.2t^2

Solution for 40,000=134t+8.2t^2 equation:

40.000=134t+8.2t^2

We move all terms to the left:

40.000-(134t+8.2t^2)=0

We add all the numbers together, and all the variables

-(134t+8.2t^2)+40=0

We get rid of parentheses

-8.2t^2-134t+40=0

a = -8.2; b = -134; c = +40;
Δ = b2-4ac
Δ = -1342-4·(-8.2)·40
Δ = 19268
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:

$\sqrt{\Delta}=\sqrt{19268}=\sqrt{4*4817}=\sqrt{4}*\sqrt{4817}=2\sqrt{4817}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-134)-2\sqrt{4817}}{2*-8.2}=\frac{134-2\sqrt{4817}}{-16.4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-134)+2\sqrt{4817}}{2*-8.2}=\frac{134+2\sqrt{4817}}{-16.4}
$