5/6x-x=-7

Solution for 5/6x-x=-7 equation:

5/6x-x=-7

We move all terms to the left:

5/6x-x-(-7)=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+5/6x+7=0

We multiply all the terms by the denominator


-1x*6x+7*6x+5=0

Wy multiply elements

-6x^2+42x+5=0

a = -6; b = 42; c = +5;
Δ = b2-4ac
Δ = 422-4·(-6)·5
Δ = 1884
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:

$\sqrt{\Delta}=\sqrt{1884}=\sqrt{4*471}=\sqrt{4}*\sqrt{471}=2\sqrt{471}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{471}}{2*-6}=\frac{-42-2\sqrt{471}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{471}}{2*-6}=\frac{-42+2\sqrt{471}}{-12}
$