5x2-18x=9

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Solution for 5x2-18x=9 equation:



5x^2-18x=9
We move all terms to the left:
5x^2-18x-(9)=0
a = 5; b = -18; c = -9;
Δ = b2-4ac
Δ = -182-4·5·(-9)
Δ = 504
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:
$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{14}}{2*5}=\frac{18-6\sqrt{14}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{14}}{2*5}=\frac{18+6\sqrt{14}}{10} $

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