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-3x(x-2)+9x=6
We move all terms to the left:
-3x(x-2)+9x-(6)=0
We add all the numbers together, and all the variables
9x-3x(x-2)-6=0
We multiply parentheses
-3x^2+9x+6x-6=0
We add all the numbers together, and all the variables
-3x^2+15x-6=0
a = -3; b = 15; c = -6;
Δ = b2-4ac
Δ = 152-4·(-3)·(-6)
Δ = 153
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{17}}{2*-3}=\frac{-15-3\sqrt{17}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{17}}{2*-3}=\frac{-15+3\sqrt{17}}{-6} $
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