(t*t)-t/2=66

Solution for (t*t)-t/2=66 equation:

(t*t)-t/2=66

We move all terms to the left:

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

We add all the numbers together, and all the variables

(+t*t)-t/2-66=0

We get rid of parentheses

t*t-t/2-66=0

We multiply all the terms by the denominator


(t*t)*2-t-66*2=0

We add all the numbers together, and all the variables

(+t*t)*2-t-66*2=0

We add all the numbers together, and all the variables

-1t+(+t*t)*2-132=0

We multiply parentheses

2t^2-1t-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}
$