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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

5x^2-15x-(-3x+9)=0

We get rid of parentheses

5x^2-15x+3x-9=0

We add all the numbers together, and all the variables

5x^2-12x-9=0

a = 5; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·5·(-9)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-18}{2*5}=\frac{-6}{10}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+18}{2*5}=\frac{30}{10}
=3
$