57/60x+9=x

Solution for 57/60x+9=x equation:

57/60x+9=x

We move all terms to the left:

57/60x+9-(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+57/60x+9=0

We multiply all the terms by the denominator


-1x*60x+9*60x+57=0

Wy multiply elements

-60x^2+540x+57=0

a = -60; b = 540; c = +57;
Δ = b2-4ac
Δ = 5402-4·(-60)·57
Δ = 305280
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:

$\sqrt{\Delta}=\sqrt{305280}=\sqrt{576*530}=\sqrt{576}*\sqrt{530}=24\sqrt{530}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(540)-24\sqrt{530}}{2*-60}=\frac{-540-24\sqrt{530}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(540)+24\sqrt{530}}{2*-60}=\frac{-540+24\sqrt{530}}{-120}
$