t^2-2t-10=200

Solution for t^2-2t-10=200 equation:

t^2-2t-10=200

We move all terms to the left:

t^2-2t-10-(200)=0

We add all the numbers together, and all the variables

t^2-2t-210=0

a = 1; b = -2; c = -210;
Δ = b2-4ac
Δ = -22-4·1·(-210)
Δ = 844
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:

$\sqrt{\Delta}=\sqrt{844}=\sqrt{4*211}=\sqrt{4}*\sqrt{211}=2\sqrt{211}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{211}}{2*1}=\frac{2-2\sqrt{211}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{211}}{2*1}=\frac{2+2\sqrt{211}}{2}
$