(9c-5)(-6c+7)=0

Solution for (9c-5)(-6c+7)=0 equation:

(9c-5)(-6c+7)=0

We multiply parentheses ..

(-54c^2+63c+30c-35)=0

We get rid of parentheses

-54c^2+63c+30c-35=0

We add all the numbers together, and all the variables

-54c^2+93c-35=0

a = -54; b = 93; c = -35;
Δ = b2-4ac
Δ = 932-4·(-54)·(-35)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(93)-33}{2*-54}=\frac{-126}{-108}
=1+1/6$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(93)+33}{2*-54}=\frac{-60}{-108}
=5/9$