30t^2-t=1

Solution for 30t^2-t=1 equation:

30t^2-t=1

We move all terms to the left:

30t^2-t-(1)=0

We add all the numbers together, and all the variables

30t^2-1t-1=0

a = 30; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·30·(-1)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*30}=\frac{-10}{60}
=-1/6
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*30}=\frac{12}{60}
=1/5
$