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3x-6(3-4x)=9x^2
We move all terms to the left:
3x-6(3-4x)-(9x^2)=0
determiningTheFunctionDomain -9x^2+3x-6(3-4x)=0
We add all the numbers together, and all the variables
-9x^2+3x-6(-4x+3)=0
We multiply parentheses
-9x^2+3x+24x-18=0
We add all the numbers together, and all the variables
-9x^2+27x-18=0
a = -9; b = 27; c = -18;
Δ = b2-4ac
Δ = 272-4·(-9)·(-18)
Δ = 81
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{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-9}{2*-9}=\frac{-36}{-18} =+2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+9}{2*-9}=\frac{-18}{-18} =1 $
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