7/6x=420x=360

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Solution for 7/6x=420x=360 equation:



7/6x=420x=360
We move all terms to the left:
7/6x-(420x)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
We add all the numbers together, and all the variables
-420x+7/6x=0
We multiply all the terms by the denominator
-420x*6x+7=0
Wy multiply elements
-2520x^2+7=0
a = -2520; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-2520)·7
Δ = 70560
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:
$\sqrt{\Delta}=\sqrt{70560}=\sqrt{7056*10}=\sqrt{7056}*\sqrt{10}=84\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-84\sqrt{10}}{2*-2520}=\frac{0-84\sqrt{10}}{-5040} =-\frac{84\sqrt{10}}{-5040} =-\frac{\sqrt{10}}{-60} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+84\sqrt{10}}{2*-2520}=\frac{0+84\sqrt{10}}{-5040} =\frac{84\sqrt{10}}{-5040} =\frac{\sqrt{10}}{-60} $

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