5t(9t-5)=0

Solution for 5t(9t-5)=0 equation:

5t(9t-5)=0

We multiply parentheses

45t^2-25t=0

a = 45; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·45·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*45}=\frac{0}{90}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*45}=\frac{50}{90}
=5/9
$