9t^2-4t+1=4t

Solution for 9t^2-4t+1=4t equation:

9t^2-4t+1=4t

We move all terms to the left:

9t^2-4t+1-(4t)=0

We add all the numbers together, and all the variables

9t^2-8t+1=0

a = 9; b = -8; c = +1;
Δ = b2-4ac
Δ = -82-4·9·1
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{7}}{2*9}=\frac{8-2\sqrt{7}}{18}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{7}}{2*9}=\frac{8+2\sqrt{7}}{18}
$