4/7x+6=x

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

4/7x+6=x

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4/7x+6=0

We multiply all the terms by the denominator


-1x*7x+6*7x+4=0

Wy multiply elements

-7x^2+42x+4=0

a = -7; b = 42; c = +4;
Δ = b2-4ac
Δ = 422-4·(-7)·4
Δ = 1876
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:

$\sqrt{\Delta}=\sqrt{1876}=\sqrt{4*469}=\sqrt{4}*\sqrt{469}=2\sqrt{469}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{469}}{2*-7}=\frac{-42-2\sqrt{469}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{469}}{2*-7}=\frac{-42+2\sqrt{469}}{-14}
$