80t+2t^2=1250

Solution for 80t+2t^2=1250 equation:

80t+2t^2=1250

We move all terms to the left:

80t+2t^2-(1250)=0

a = 2; b = 80; c = -1250;
Δ = b2-4ac
Δ = 802-4·2·(-1250)
Δ = 16400
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:

$\sqrt{\Delta}=\sqrt{16400}=\sqrt{400*41}=\sqrt{400}*\sqrt{41}=20\sqrt{41}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-20\sqrt{41}}{2*2}=\frac{-80-20\sqrt{41}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+20\sqrt{41}}{2*2}=\frac{-80+20\sqrt{41}}{4}
$