6t=t^2-8t

Solution for 6t=t^2-8t equation:

6t=t^2-8t

We move all terms to the left:

6t-(t^2-8t)=0

We get rid of parentheses

-t^2+6t+8t=0

We add all the numbers together, and all the variables

-1t^2+14t=0

a = -1; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-1)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-1}=\frac{-28}{-2}
=+14
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-1}=\frac{0}{-2}
=0
$