4c(c-4)=9c+5

Solution for 4c(c-4)=9c+5 equation:

4c(c-4)=9c+5

We move all terms to the left:

4c(c-4)-(9c+5)=0

We multiply parentheses

4c^2-16c-(9c+5)=0

We get rid of parentheses

4c^2-16c-9c-5=0

We add all the numbers together, and all the variables

4c^2-25c-5=0

a = 4; b = -25; c = -5;
Δ = b2-4ac
Δ = -252-4·4·(-5)
Δ = 705
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-\sqrt{705}}{2*4}=\frac{25-\sqrt{705}}{8}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{705}}{2*4}=\frac{25+\sqrt{705}}{8}
$