11-4x=1/3x-19

Solution for 11-4x=1/3x-19 equation:

11-4x=1/3x-19

We move all terms to the left:

11-4x-(1/3x-19)=0


Domain of the equation: 3x-19)!=0

x∈R


We get rid of parentheses

-4x-1/3x+19+11=0

We multiply all the terms by the denominator


-4x*3x+19*3x+11*3x-1=0

Wy multiply elements

-12x^2+57x+33x-1=0

We add all the numbers together, and all the variables

-12x^2+90x-1=0

a = -12; b = 90; c = -1;
Δ = b2-4ac
Δ = 902-4·(-12)·(-1)
Δ = 8052
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:

$\sqrt{\Delta}=\sqrt{8052}=\sqrt{4*2013}=\sqrt{4}*\sqrt{2013}=2\sqrt{2013}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{2013}}{2*-12}=\frac{-90-2\sqrt{2013}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{2013}}{2*-12}=\frac{-90+2\sqrt{2013}}{-24}
$