10/7x-60=x

Solution for 10/7x-60=x equation:

10/7x-60=x

We move all terms to the left:

10/7x-60-(x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+10/7x-60=0

We multiply all the terms by the denominator


-1x*7x-60*7x+10=0

Wy multiply elements

-7x^2-420x+10=0

a = -7; b = -420; c = +10;
Δ = b2-4ac
Δ = -4202-4·(-7)·10
Δ = 176680
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:

$\sqrt{\Delta}=\sqrt{176680}=\sqrt{4*44170}=\sqrt{4}*\sqrt{44170}=2\sqrt{44170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-2\sqrt{44170}}{2*-7}=\frac{420-2\sqrt{44170}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+2\sqrt{44170}}{2*-7}=\frac{420+2\sqrt{44170}}{-14}
$