7/6x=140x=

Solution for 7/6x=140x= equation:

7/6x=140x=

We move all terms to the left:

7/6x-(140x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-140x+7/6x=0

We multiply all the terms by the denominator


-140x*6x+7=0

Wy multiply elements

-840x^2+7=0

a = -840; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-840)·7
Δ = 23520
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:

$\sqrt{\Delta}=\sqrt{23520}=\sqrt{784*30}=\sqrt{784}*\sqrt{30}=28\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{30}}{2*-840}=\frac{0-28\sqrt{30}}{-1680}
=-\frac{28\sqrt{30}}{-1680}
=-\frac{\sqrt{30}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{30}}{2*-840}=\frac{0+28\sqrt{30}}{-1680}
=\frac{28\sqrt{30}}{-1680}
=\frac{\sqrt{30}}{-60}
$