8t-t^2=8

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

8t-t^2=8

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1t^2+8t-8=0

a = -1; b = 8; c = -8;
Δ = b2-4ac
Δ = 82-4·(-1)·(-8)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{2}}{2*-1}=\frac{-8-4\sqrt{2}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{2}}{2*-1}=\frac{-8+4\sqrt{2}}{-2}
$