-9(x-9)=3x(x+47)

Solution for -9(x-9)=3x(x+47) equation:

-9(x-9)=3x(x+47)

We move all terms to the left:

-9(x-9)-(3x(x+47))=0

We multiply parentheses

-9x-(3x(x+47))+81=0


We calculate terms in parentheses: -(3x(x+47)), so:

3x(x+47)

We multiply parentheses

3x^2+141x

Back to the equation:

-(3x^2+141x)


We get rid of parentheses

-3x^2-9x-141x+81=0

We add all the numbers together, and all the variables

-3x^2-150x+81=0

a = -3; b = -150; c = +81;
Δ = b2-4ac
Δ = -1502-4·(-3)·81
Δ = 23472
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{23472}=\sqrt{144*163}=\sqrt{144}*\sqrt{163}=12\sqrt{163}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-12\sqrt{163}}{2*-3}=\frac{150-12\sqrt{163}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+12\sqrt{163}}{2*-3}=\frac{150+12\sqrt{163}}{-6}
$