6t(3t-5)=0

Solution for 6t(3t-5)=0 equation:

6t(3t-5)=0

We multiply parentheses

18t^2-30t=0

a = 18; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·18·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*18}=\frac{0}{36}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*18}=\frac{60}{36}
=1+2/3
$