t=-(t2-3t-10)

Solution for t=-(t2-3t-10) equation:

t=-(t2-3t-10)

We move all terms to the left:

t-(-(t2-3t-10))=0

We add all the numbers together, and all the variables

-(-(+t^2-3t-10))+t=0


We calculate terms in parentheses: -(-(+t^2-3t-10)), so:

-(+t^2-3t-10)

We get rid of parentheses

-t^2+3t+10

We add all the numbers together, and all the variables

-1t^2+3t+10

Back to the equation:

-(-1t^2+3t+10)


We get rid of parentheses

1t^2-3t+t-10=0

We add all the numbers together, and all the variables

t^2-2t-10=0

a = 1; b = -2; c = -10;
Δ = b2-4ac
Δ = -22-4·1·(-10)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{11}}{2*1}=\frac{2-2\sqrt{11}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{11}}{2*1}=\frac{2+2\sqrt{11}}{2}
$