47/60x+26=x

Solution for 47/60x+26=x equation:

47/60x+26=x

We move all terms to the left:

47/60x+26-(x)=0


Domain of the equation: 60x!=0

x!=0/60

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+47/60x+26=0

We multiply all the terms by the denominator


-1x*60x+26*60x+47=0

Wy multiply elements

-60x^2+1560x+47=0

a = -60; b = 1560; c = +47;
Δ = b2-4ac
Δ = 15602-4·(-60)·47
Δ = 2444880
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:

$\sqrt{\Delta}=\sqrt{2444880}=\sqrt{16*152805}=\sqrt{16}*\sqrt{152805}=4\sqrt{152805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1560)-4\sqrt{152805}}{2*-60}=\frac{-1560-4\sqrt{152805}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1560)+4\sqrt{152805}}{2*-60}=\frac{-1560+4\sqrt{152805}}{-120}
$