6c(3c-1)=60

Solution for 6c(3c-1)=60 equation:

6c(3c-1)=60

We move all terms to the left:

6c(3c-1)-(60)=0

We multiply parentheses

18c^2-6c-60=0

a = 18; b = -6; c = -60;
Δ = b2-4ac
Δ = -62-4·18·(-60)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-66}{2*18}=\frac{-60}{36}
=-1+2/3
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+66}{2*18}=\frac{72}{36}
=2
$