1/2x-19=11x=

Solution for 1/2x-19=11x= equation:

1/2x-19=11x=

We move all terms to the left:

1/2x-19-(11x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-11x+1/2x-19=0

We multiply all the terms by the denominator


-11x*2x-19*2x+1=0

Wy multiply elements

-22x^2-38x+1=0

a = -22; b = -38; c = +1;
Δ = b2-4ac
Δ = -382-4·(-22)·1
Δ = 1532
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:

$\sqrt{\Delta}=\sqrt{1532}=\sqrt{4*383}=\sqrt{4}*\sqrt{383}=2\sqrt{383}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-2\sqrt{383}}{2*-22}=\frac{38-2\sqrt{383}}{-44}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+2\sqrt{383}}{2*-22}=\frac{38+2\sqrt{383}}{-44}
$