-6c^2=-60+9c

Solution for -6c^2=-60+9c equation:

-6c^2=-60+9c

We move all terms to the left:

-6c^2-(-60+9c)=0

We add all the numbers together, and all the variables

-6c^2-(9c-60)=0

We get rid of parentheses

-6c^2-9c+60=0

a = -6; b = -9; c = +60;
Δ = b2-4ac
Δ = -92-4·(-6)·60
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-39}{2*-6}=\frac{-30}{-12}
=2+1/2
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+39}{2*-6}=\frac{48}{-12}
=-4
$