x2-10x-54=0

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Solution for x2-10x-54=0 equation:



x2-10x-54=0
We add all the numbers together, and all the variables
x^2-10x-54=0
a = 1; b = -10; c = -54;
Δ = b2-4ac
Δ = -102-4·1·(-54)
Δ = 316
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:
$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{79}}{2*1}=\frac{10-2\sqrt{79}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{79}}{2*1}=\frac{10+2\sqrt{79}}{2} $

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