8t^2=1-10t

Solution for 8t^2=1-10t equation:

8t^2=1-10t

We move all terms to the left:

8t^2-(1-10t)=0

We add all the numbers together, and all the variables

8t^2-(-10t+1)=0

We get rid of parentheses

8t^2+10t-1=0

a = 8; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·8·(-1)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{33}}{2*8}=\frac{-10-2\sqrt{33}}{16}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{33}}{2*8}=\frac{-10+2\sqrt{33}}{16}
$