37/60x+23=x

Solution for 37/60x+23=x equation:

37/60x+23=x

We move all terms to the left:

37/60x+23-(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+37/60x+23=0

We multiply all the terms by the denominator


-1x*60x+23*60x+37=0

Wy multiply elements

-60x^2+1380x+37=0

a = -60; b = 1380; c = +37;
Δ = b2-4ac
Δ = 13802-4·(-60)·37
Δ = 1913280
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:

$\sqrt{\Delta}=\sqrt{1913280}=\sqrt{64*29895}=\sqrt{64}*\sqrt{29895}=8\sqrt{29895}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1380)-8\sqrt{29895}}{2*-60}=\frac{-1380-8\sqrt{29895}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1380)+8\sqrt{29895}}{2*-60}=\frac{-1380+8\sqrt{29895}}{-120}
$