8t^2=1-2t

Solution for 8t^2=1-2t equation:

8t^2=1-2t

We move all terms to the left:

8t^2-(1-2t)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

8t^2+2t-1=0

a = 8; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·8·(-1)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*8}=\frac{-8}{16}
=-1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*8}=\frac{4}{16}
=1/4
$