5c(c-2)=3(c+2)

Solution for 5c(c-2)=3(c+2) equation:

5c(c-2)=3(c+2)

We move all terms to the left:

5c(c-2)-(3(c+2))=0

We multiply parentheses

5c^2-10c-(3(c+2))=0


We calculate terms in parentheses: -(3(c+2)), so:

3(c+2)

We multiply parentheses

3c+6

Back to the equation:

-(3c+6)


We get rid of parentheses

5c^2-10c-3c-6=0

We add all the numbers together, and all the variables

5c^2-13c-6=0

a = 5; b = -13; c = -6;
Δ = b2-4ac
Δ = -132-4·5·(-6)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-17}{2*5}=\frac{-4}{10}
=-2/5
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+17}{2*5}=\frac{30}{10}
=3
$