66=t^2-t/2

Solution for 66=t^2-t/2 equation:

66=t^2-t/2

We move all terms to the left:

66-(t^2-t/2)=0

We get rid of parentheses

-t^2+t/2+66=0

We multiply all the terms by the denominator


-t^2*2+t+66*2=0

We add all the numbers together, and all the variables

-t^2*2+t+132=0

Wy multiply elements

-2t^2+t+132=0

a = -2; b = 1; c = +132;
Δ = b2-4ac
Δ = 12-4·(-2)·132
Δ = 1057
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{1057}}{2*-2}=\frac{-1-\sqrt{1057}}{-4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1057}}{2*-2}=\frac{-1+\sqrt{1057}}{-4}
$