6t(5t-5)=5

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

6t(5t-5)=5

We move all terms to the left:

6t(5t-5)-(5)=0

We multiply parentheses

30t^2-30t-5=0

a = 30; b = -30; c = -5;
Δ = b2-4ac
Δ = -302-4·30·(-5)
Δ = 1500
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:

$\sqrt{\Delta}=\sqrt{1500}=\sqrt{100*15}=\sqrt{100}*\sqrt{15}=10\sqrt{15}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{15}}{2*30}=\frac{30-10\sqrt{15}}{60}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{15}}{2*30}=\frac{30+10\sqrt{15}}{60}
$