(5/13)x=36

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Solution for (5/13)x=36 equation:



(5/13)x=36
We move all terms to the left:
(5/13)x-(36)=0
Domain of the equation: 13)x!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+5/13)x-36=0
We multiply parentheses
5x^2-36=0
a = 5; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·5·(-36)
Δ = 720
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:
$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*5}=\frac{0-12\sqrt{5}}{10} =-\frac{12\sqrt{5}}{10} =-\frac{6\sqrt{5}}{5} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*5}=\frac{0+12\sqrt{5}}{10} =\frac{12\sqrt{5}}{10} =\frac{6\sqrt{5}}{5} $

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