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3x(-5x+9)=9
We move all terms to the left:
3x(-5x+9)-(9)=0
We multiply parentheses
-15x^2+27x-9=0
a = -15; b = 27; c = -9;
Δ = b2-4ac
Δ = 272-4·(-15)·(-9)
Δ = 189
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{21}}{2*-15}=\frac{-27-3\sqrt{21}}{-30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{21}}{2*-15}=\frac{-27+3\sqrt{21}}{-30} $
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