59/60x+1=x

Solution for 59/60x+1=x equation:

59/60x+1=x

We move all terms to the left:

59/60x+1-(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+59/60x+1=0

We multiply all the terms by the denominator


-1x*60x+1*60x+59=0

Wy multiply elements

-60x^2+60x+59=0

a = -60; b = 60; c = +59;
Δ = b2-4ac
Δ = 602-4·(-60)·59
Δ = 17760
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:

$\sqrt{\Delta}=\sqrt{17760}=\sqrt{16*1110}=\sqrt{16}*\sqrt{1110}=4\sqrt{1110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{1110}}{2*-60}=\frac{-60-4\sqrt{1110}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{1110}}{2*-60}=\frac{-60+4\sqrt{1110}}{-120}
$