-2(9r+3)-7r=-10r(12r+9)

Solution for -2(9r+3)-7r=-10r(12r+9) equation:

-2(9r+3)-7r=-10r(12r+9)

We move all terms to the left:

-2(9r+3)-7r-(-10r(12r+9))=0

We add all the numbers together, and all the variables

-7r-2(9r+3)-(-10r(12r+9))=0

We multiply parentheses

-7r-18r-(-10r(12r+9))-6=0


We calculate terms in parentheses: -(-10r(12r+9)), so:

-10r(12r+9)

We multiply parentheses

-120r^2-90r

Back to the equation:

-(-120r^2-90r)


We add all the numbers together, and all the variables

-(-120r^2-90r)-25r-6=0

We get rid of parentheses

120r^2+90r-25r-6=0

We add all the numbers together, and all the variables

120r^2+65r-6=0

a = 120; b = 65; c = -6;
Δ = b2-4ac
Δ = 652-4·120·(-6)
Δ = 7105
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:

$\sqrt{\Delta}=\sqrt{7105}=\sqrt{49*145}=\sqrt{49}*\sqrt{145}=7\sqrt{145}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-7\sqrt{145}}{2*120}=\frac{-65-7\sqrt{145}}{240}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+7\sqrt{145}}{2*120}=\frac{-65+7\sqrt{145}}{240}
$