43/60x+680=x

Solution for 43/60x+680=x equation:

43/60x+680=x

We move all terms to the left:

43/60x+680-(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+43/60x+680=0

We multiply all the terms by the denominator


-1x*60x+680*60x+43=0

Wy multiply elements

-60x^2+40800x+43=0

a = -60; b = 40800; c = +43;
Δ = b2-4ac
Δ = 408002-4·(-60)·43
Δ = 1664650320
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:

$\sqrt{\Delta}=\sqrt{1664650320}=\sqrt{16*104040645}=\sqrt{16}*\sqrt{104040645}=4\sqrt{104040645}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40800)-4\sqrt{104040645}}{2*-60}=\frac{-40800-4\sqrt{104040645}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40800)+4\sqrt{104040645}}{2*-60}=\frac{-40800+4\sqrt{104040645}}{-120}
$