z+2/z-8=11z-4

Solution for z+2/z-8=11z-4 equation:

z+2/z-8=11z-4

We move all terms to the left:

z+2/z-8-(11z-4)=0


Domain of the equation: z!=0

z∈R


We get rid of parentheses

z+2/z-11z+4-8=0

We multiply all the terms by the denominator


z*z-11z*z+4*z-8*z+2=0

We add all the numbers together, and all the variables

-4z+z*z-11z*z+2=0

Wy multiply elements

z^2-11z^2-4z+2=0

We add all the numbers together, and all the variables

-10z^2-4z+2=0

a = -10; b = -4; c = +2;
Δ = b2-4ac
Δ = -42-4·(-10)·2
Δ = 96
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{6}}{2*-10}=\frac{4-4\sqrt{6}}{-20}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{6}}{2*-10}=\frac{4+4\sqrt{6}}{-20}
$