9t(2t-4)=25

Solution for 9t(2t-4)=25 equation:

9t(2t-4)=25

We move all terms to the left:

9t(2t-4)-(25)=0

We multiply parentheses

18t^2-36t-25=0

a = 18; b = -36; c = -25;
Δ = b2-4ac
Δ = -362-4·18·(-25)
Δ = 3096
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:

$\sqrt{\Delta}=\sqrt{3096}=\sqrt{36*86}=\sqrt{36}*\sqrt{86}=6\sqrt{86}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{86}}{2*18}=\frac{36-6\sqrt{86}}{36}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{86}}{2*18}=\frac{36+6\sqrt{86}}{36}
$