111-7/6x=5x

Solution for 111-7/6x=5x equation:

111-7/6x=5x

We move all terms to the left:

111-7/6x-(5x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-5x-7/6x+111=0

We multiply all the terms by the denominator


-5x*6x+111*6x-7=0

Wy multiply elements

-30x^2+666x-7=0

a = -30; b = 666; c = -7;
Δ = b2-4ac
Δ = 6662-4·(-30)·(-7)
Δ = 442716
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:

$\sqrt{\Delta}=\sqrt{442716}=\sqrt{4*110679}=\sqrt{4}*\sqrt{110679}=2\sqrt{110679}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(666)-2\sqrt{110679}}{2*-30}=\frac{-666-2\sqrt{110679}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(666)+2\sqrt{110679}}{2*-30}=\frac{-666+2\sqrt{110679}}{-60}
$