9t2=36t-1

Solution for 9t2=36t-1 equation:

9t^2=36t-1

We move all terms to the left:

9t^2-(36t-1)=0

We get rid of parentheses

9t^2-36t+1=0

a = 9; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·9·1
Δ = 1260
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:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{35}}{2*9}=\frac{36-6\sqrt{35}}{18}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{35}}{2*9}=\frac{36+6\sqrt{35}}{18}
$