-8t^2+16t=-8

Solution for -8t^2+16t=-8 equation:

-8t^2+16t=-8

We move all terms to the left:

-8t^2+16t-(-8)=0

We add all the numbers together, and all the variables

-8t^2+16t+8=0

a = -8; b = 16; c = +8;
Δ = b2-4ac
Δ = 162-4·(-8)·8
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16\sqrt{2}}{2*-8}=\frac{-16-16\sqrt{2}}{-16}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16\sqrt{2}}{2*-8}=\frac{-16+16\sqrt{2}}{-16}
$