-3x(x-9)=5x-3(x+2)

Solution for -3x(x-9)=5x-3(x+2) equation:

-3x(x-9)=5x-3(x+2)

We move all terms to the left:

-3x(x-9)-(5x-3(x+2))=0

We multiply parentheses

-3x^2+27x-(5x-3(x+2))=0


We calculate terms in parentheses: -(5x-3(x+2)), so:

5x-3(x+2)

We multiply parentheses

5x-3x-6

We add all the numbers together, and all the variables

2x-6

Back to the equation:

-(2x-6)


We get rid of parentheses

-3x^2+27x-2x+6=0

We add all the numbers together, and all the variables

-3x^2+25x+6=0

a = -3; b = 25; c = +6;
Δ = b2-4ac
Δ = 252-4·(-3)·6
Δ = 697
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{697}}{2*-3}=\frac{-25-\sqrt{697}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{697}}{2*-3}=\frac{-25+\sqrt{697}}{-6}
$