75+54x+9x^2=0

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Solution for 75+54x+9x^2=0 equation:



75+54x+9x^2=0
a = 9; b = 54; c = +75;
Δ = b2-4ac
Δ = 542-4·9·75
Δ = 216
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:
$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{6}}{2*9}=\frac{-54-6\sqrt{6}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{6}}{2*9}=\frac{-54+6\sqrt{6}}{18} $

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