z+4=1/23z-11

Solution for z+4=1/23z-11 equation:

z+4=1/23z-11

We move all terms to the left:

z+4-(1/23z-11)=0


Domain of the equation: 23z-11)!=0

z∈R


We get rid of parentheses

z-1/23z+11+4=0

We multiply all the terms by the denominator


z*23z+11*23z+4*23z-1=0

Wy multiply elements

23z^2+253z+92z-1=0

We add all the numbers together, and all the variables

23z^2+345z-1=0

a = 23; b = 345; c = -1;
Δ = b2-4ac
Δ = 3452-4·23·(-1)
Δ = 119117
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(345)-\sqrt{119117}}{2*23}=\frac{-345-\sqrt{119117}}{46}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(345)+\sqrt{119117}}{2*23}=\frac{-345+\sqrt{119117}}{46}
$