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

Solution for 0=-(t^2-t-30) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(-(t^2-t-30)), so:

-(t^2-t-30)

We get rid of parentheses

-t^2+t+30

We add all the numbers together, and all the variables

-1t^2+t+30

Back to the equation:

-(-1t^2+t+30)


We get rid of parentheses

1t^2-t-30=0

We add all the numbers together, and all the variables

t^2-1t-30=0

a = 1; b = -1; c = -30;
Δ = b2-4ac
Δ = -12-4·1·(-30)
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*1}=\frac{-10}{2}
=-5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*1}=\frac{12}{2}
=6
$