2(9r+4)+8(9r+4)=(18r+8)(9r+4)

Solution for 2(9r+4)+8(9r+4)=(18r+8)(9r+4) equation:

2(9r+4)+8(9r+4)=(18r+8)(9r+4)

We move all terms to the left:

2(9r+4)+8(9r+4)-((18r+8)(9r+4))=0

We multiply parentheses

18r+72r-((18r+8)(9r+4))+8+32=0

We multiply parentheses ..

-((+162r^2+72r+72r+32))+18r+72r+8+32=0


We calculate terms in parentheses: -((+162r^2+72r+72r+32)), so:

(+162r^2+72r+72r+32)

We get rid of parentheses

162r^2+72r+72r+32

We add all the numbers together, and all the variables

162r^2+144r+32

Back to the equation:

-(162r^2+144r+32)


We add all the numbers together, and all the variables

90r-(162r^2+144r+32)+40=0

We get rid of parentheses

-162r^2+90r-144r-32+40=0

We add all the numbers together, and all the variables

-162r^2-54r+8=0

a = -162; b = -54; c = +8;
Δ = b2-4ac
Δ = -542-4·(-162)·8
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-90}{2*-162}=\frac{-36}{-324}
=1/9
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+90}{2*-162}=\frac{144}{-324}
=-4/9
$