23/19x-x=260

Solution for 23/19x-x=260 equation:

23/19x-x=260

We move all terms to the left:

23/19x-x-(260)=0


Domain of the equation: 19x!=0

x!=0/19

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+23/19x-260=0

We multiply all the terms by the denominator


-1x*19x-260*19x+23=0

Wy multiply elements

-19x^2-4940x+23=0

a = -19; b = -4940; c = +23;
Δ = b2-4ac
Δ = -49402-4·(-19)·23
Δ = 24405348
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:

$\sqrt{\Delta}=\sqrt{24405348}=\sqrt{4*6101337}=\sqrt{4}*\sqrt{6101337}=2\sqrt{6101337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4940)-2\sqrt{6101337}}{2*-19}=\frac{4940-2\sqrt{6101337}}{-38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4940)+2\sqrt{6101337}}{2*-19}=\frac{4940+2\sqrt{6101337}}{-38}
$