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3x(3x-9)=5670
We move all terms to the left:
3x(3x-9)-(5670)=0
We multiply parentheses
9x^2-27x-5670=0
a = 9; b = -27; c = -5670;
Δ = b2-4ac
Δ = -272-4·9·(-5670)
Δ = 204849
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{204849}=\sqrt{729*281}=\sqrt{729}*\sqrt{281}=27\sqrt{281}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27\sqrt{281}}{2*9}=\frac{27-27\sqrt{281}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27\sqrt{281}}{2*9}=\frac{27+27\sqrt{281}}{18} $
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