5x*x-54x-225=0

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Solution for 5x*x-54x-225=0 equation:



5x*x-54x-225=0
We add all the numbers together, and all the variables
-54x+5x*x-225=0
Wy multiply elements
5x^2-54x-225=0
a = 5; b = -54; c = -225;
Δ = b2-4ac
Δ = -542-4·5·(-225)
Δ = 7416
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:
$\sqrt{\Delta}=\sqrt{7416}=\sqrt{36*206}=\sqrt{36}*\sqrt{206}=6\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{206}}{2*5}=\frac{54-6\sqrt{206}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{206}}{2*5}=\frac{54+6\sqrt{206}}{10} $

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