3/5x=12x=

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Solution for 3/5x=12x= equation:



3/5x=12x=
We move all terms to the left:
3/5x-(12x)=0
Domain of the equation: 5x!=0
x!=0/5
x!=0
x∈R
We add all the numbers together, and all the variables
-12x+3/5x=0
We multiply all the terms by the denominator
-12x*5x+3=0
Wy multiply elements
-60x^2+3=0
a = -60; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-60)·3
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*-60}=\frac{0-12\sqrt{5}}{-120} =-\frac{12\sqrt{5}}{-120} =-\frac{\sqrt{5}}{-10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*-60}=\frac{0+12\sqrt{5}}{-120} =\frac{12\sqrt{5}}{-120} =\frac{\sqrt{5}}{-10} $

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