4/7x+912=x

Solution for 4/7x+912=x equation:

4/7x+912=x

We move all terms to the left:

4/7x+912-(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+912=0

We multiply all the terms by the denominator


-1x*7x+912*7x+4=0

Wy multiply elements

-7x^2+6384x+4=0

a = -7; b = 6384; c = +4;
Δ = b2-4ac
Δ = 63842-4·(-7)·4
Δ = 40755568
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:

$\sqrt{\Delta}=\sqrt{40755568}=\sqrt{16*2547223}=\sqrt{16}*\sqrt{2547223}=4\sqrt{2547223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6384)-4\sqrt{2547223}}{2*-7}=\frac{-6384-4\sqrt{2547223}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6384)+4\sqrt{2547223}}{2*-7}=\frac{-6384+4\sqrt{2547223}}{-14}
$