1=30t-t*t

Solution for 1=30t-t*t equation:

1=30t-t*t

We move all terms to the left:

1-(30t-t*t)=0

We add all the numbers together, and all the variables

-(+30t-t*t)+1=0

We get rid of parentheses

-30t+t*t+1=0

Wy multiply elements

t^2-30t+1=0

a = 1; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·1·1
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-8\sqrt{14}}{2*1}=\frac{30-8\sqrt{14}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+8\sqrt{14}}{2*1}=\frac{30+8\sqrt{14}}{2}
$