z-6/2z+1=10.

Solution for z-6/2z+1=10. equation:

z-6/2z+1=10.

We move all terms to the left:

z-6/2z+1-(10.)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We add all the numbers together, and all the variables

z-6/2z+1-10=0

We add all the numbers together, and all the variables

z-6/2z-9=0

We multiply all the terms by the denominator


z*2z-9*2z-6=0

Wy multiply elements

2z^2-18z-6=0

a = 2; b = -18; c = -6;
Δ = b2-4ac
Δ = -182-4·2·(-6)
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{93}}{2*2}=\frac{18-2\sqrt{93}}{4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{93}}{2*2}=\frac{18+2\sqrt{93}}{4}
$