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

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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 $

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