1/2(z)+5=11z=

Solution for 1/2(z)+5=11z= equation:

1/2(z)+5=11z=

We move all terms to the left:

1/2(z)+5-(11z)=0


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We add all the numbers together, and all the variables

-11z+1/2z+5=0

We multiply all the terms by the denominator


-11z*2z+5*2z+1=0

Wy multiply elements

-22z^2+10z+1=0

a = -22; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-22)·1
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{47}}{2*-22}=\frac{-10-2\sqrt{47}}{-44}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{47}}{2*-22}=\frac{-10+2\sqrt{47}}{-44}
$