r(r-6)=3(7-2r)

Solution for r(r-6)=3(7-2r) equation:

r(r-6)=3(7-2r)

We move all terms to the left:

r(r-6)-(3(7-2r))=0

We add all the numbers together, and all the variables

r(r-6)-(3(-2r+7))=0

We multiply parentheses

r^2-6r-(3(-2r+7))=0


We calculate terms in parentheses: -(3(-2r+7)), so:

3(-2r+7)

We multiply parentheses

-6r+21

Back to the equation:

-(-6r+21)


We get rid of parentheses

r^2-6r+6r-21=0

We add all the numbers together, and all the variables

r^2-21=0

a = 1; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·1·(-21)
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*1}=\frac{0-2\sqrt{21}}{2}
=-\frac{2\sqrt{21}}{2}
=-\sqrt{21}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*1}=\frac{0+2\sqrt{21}}{2}
=\frac{2\sqrt{21}}{2}
=\sqrt{21}
$