(5-3c)-(4c+6)=(8c+11)(3c-6)

Solution for (5-3c)-(4c+6)=(8c+11)(3c-6) equation:

(5-3c)-(4c+6)=(8c+11)(3c-6)

We move all terms to the left:

(5-3c)-(4c+6)-((8c+11)(3c-6))=0

We add all the numbers together, and all the variables

(-3c+5)-(4c+6)-((8c+11)(3c-6))=0

We get rid of parentheses

-3c-4c-((8c+11)(3c-6))+5-6=0

We multiply parentheses ..

-((+24c^2-48c+33c-66))-3c-4c+5-6=0


We calculate terms in parentheses: -((+24c^2-48c+33c-66)), so:

(+24c^2-48c+33c-66)

We get rid of parentheses

24c^2-48c+33c-66

We add all the numbers together, and all the variables

24c^2-15c-66

Back to the equation:

-(24c^2-15c-66)


We add all the numbers together, and all the variables

-7c-(24c^2-15c-66)-1=0

We get rid of parentheses

-24c^2-7c+15c+66-1=0

We add all the numbers together, and all the variables

-24c^2+8c+65=0

a = -24; b = 8; c = +65;
Δ = b2-4ac
Δ = 82-4·(-24)·65
Δ = 6304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6304}=\sqrt{16*394}=\sqrt{16}*\sqrt{394}=4\sqrt{394}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{394}}{2*-24}=\frac{-8-4\sqrt{394}}{-48}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{394}}{2*-24}=\frac{-8+4\sqrt{394}}{-48}
$