7/6x-x=490

Solution for 7/6x-x=490 equation:

7/6x-x=490

We move all terms to the left:

7/6x-x-(490)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+7/6x-490=0

We multiply all the terms by the denominator


-1x*6x-490*6x+7=0

Wy multiply elements

-6x^2-2940x+7=0

a = -6; b = -2940; c = +7;
Δ = b2-4ac
Δ = -29402-4·(-6)·7
Δ = 8643768
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:

$\sqrt{\Delta}=\sqrt{8643768}=\sqrt{4*2160942}=\sqrt{4}*\sqrt{2160942}=2\sqrt{2160942}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2940)-2\sqrt{2160942}}{2*-6}=\frac{2940-2\sqrt{2160942}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2940)+2\sqrt{2160942}}{2*-6}=\frac{2940+2\sqrt{2160942}}{-12}
$