6r+36=6r(r+4)

Solution for 6r+36=6r(r+4) equation:

6r+36=6r(r+4)

We move all terms to the left:

6r+36-(6r(r+4))=0


We calculate terms in parentheses: -(6r(r+4)), so:

6r(r+4)

We multiply parentheses

6r^2+24r

Back to the equation:

-(6r^2+24r)


We get rid of parentheses

-6r^2+6r-24r+36=0

We add all the numbers together, and all the variables

-6r^2-18r+36=0

a = -6; b = -18; c = +36;
Δ = b2-4ac
Δ = -182-4·(-6)·36
Δ = 1188
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1188}=\sqrt{36*33}=\sqrt{36}*\sqrt{33}=6\sqrt{33}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{33}}{2*-6}=\frac{18-6\sqrt{33}}{-12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{33}}{2*-6}=\frac{18+6\sqrt{33}}{-12}
$