4/11x+23=X-19

Solution for 4/11x+23=X-19 equation:

4/11x+23=x-19

We move all terms to the left:

4/11x+23-(x-19)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R


We get rid of parentheses

4/11x-x+19+23=0

We multiply all the terms by the denominator


-x*11x+19*11x+23*11x+4=0

Wy multiply elements

-11x^2+209x+253x+4=0

We add all the numbers together, and all the variables

-11x^2+462x+4=0

a = -11; b = 462; c = +4;
Δ = b2-4ac
Δ = 4622-4·(-11)·4
Δ = 213620
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:

$\sqrt{\Delta}=\sqrt{213620}=\sqrt{4*53405}=\sqrt{4}*\sqrt{53405}=2\sqrt{53405}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(462)-2\sqrt{53405}}{2*-11}=\frac{-462-2\sqrt{53405}}{-22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(462)+2\sqrt{53405}}{2*-11}=\frac{-462+2\sqrt{53405}}{-22}
$