0=8t^2-57

Solution for 0=8t^2-57 equation:

0=8t^2-57

We move all terms to the left:

0-(8t^2-57)=0

We add all the numbers together, and all the variables

-(8t^2-57)=0

We get rid of parentheses

-8t^2+57=0

a = -8; b = 0; c = +57;
Δ = b2-4ac
Δ = 02-4·(-8)·57
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{114}}{2*-8}=\frac{0-4\sqrt{114}}{-16}
=-\frac{4\sqrt{114}}{-16}
=-\frac{\sqrt{114}}{-4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{114}}{2*-8}=\frac{0+4\sqrt{114}}{-16}
=\frac{4\sqrt{114}}{-16}
=\frac{\sqrt{114}}{-4}
$