t(1/2)-6t(1/4)+9=0

Solution for t(1/2)-6t(1/4)+9=0 equation:

t(1/2)-6t(1/4)+9=0

We add all the numbers together, and all the variables

t(+1/2)-6t(+1/4)+9=0

We multiply parentheses

t^2-6t^2+9=0

We add all the numbers together, and all the variables

-5t^2+9=0

a = -5; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-5)·9
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*-5}=\frac{0-6\sqrt{5}}{-10}
=-\frac{6\sqrt{5}}{-10}
=-\frac{3\sqrt{5}}{-5}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*-5}=\frac{0+6\sqrt{5}}{-10}
=\frac{6\sqrt{5}}{-10}
=\frac{3\sqrt{5}}{-5}
$