31t^2+100t=50

Solution for 31t^2+100t=50 equation:

31t^2+100t=50

We move all terms to the left:

31t^2+100t-(50)=0

a = 31; b = 100; c = -50;
Δ = b2-4ac
Δ = 1002-4·31·(-50)
Δ = 16200
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:

$\sqrt{\Delta}=\sqrt{16200}=\sqrt{8100*2}=\sqrt{8100}*\sqrt{2}=90\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-90\sqrt{2}}{2*31}=\frac{-100-90\sqrt{2}}{62}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+90\sqrt{2}}{2*31}=\frac{-100+90\sqrt{2}}{62}
$