6+5/7x=x-4

Solution for 6+5/7x=x-4 equation:

6+5/7x=x-4

We move all terms to the left:

6+5/7x-(x-4)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

5/7x-x+4+6=0

We multiply all the terms by the denominator


-x*7x+4*7x+6*7x+5=0

Wy multiply elements

-7x^2+28x+42x+5=0

We add all the numbers together, and all the variables

-7x^2+70x+5=0

a = -7; b = 70; c = +5;
Δ = b2-4ac
Δ = 702-4·(-7)·5
Δ = 5040
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:

$\sqrt{\Delta}=\sqrt{5040}=\sqrt{144*35}=\sqrt{144}*\sqrt{35}=12\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-12\sqrt{35}}{2*-7}=\frac{-70-12\sqrt{35}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+12\sqrt{35}}{2*-7}=\frac{-70+12\sqrt{35}}{-14}
$