0=8t^2-31t

Solution for 0=8t^2-31t equation:

0=8t^2-31t

We move all terms to the left:

0-(8t^2-31t)=0

We add all the numbers together, and all the variables

-(8t^2-31t)=0

We get rid of parentheses

-8t^2+31t=0

a = -8; b = 31; c = 0;
Δ = b2-4ac
Δ = 312-4·(-8)·0
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-31}{2*-8}=\frac{-62}{-16}
=3+7/8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+31}{2*-8}=\frac{0}{-16}
=0
$