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9x^2-4x-54=0
a = 9; b = -4; c = -54;
Δ = b2-4ac
Δ = -42-4·9·(-54)
Δ = 1960
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1960}=\sqrt{196*10}=\sqrt{196}*\sqrt{10}=14\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-14\sqrt{10}}{2*9}=\frac{4-14\sqrt{10}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+14\sqrt{10}}{2*9}=\frac{4+14\sqrt{10}}{18} $
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