11z-1/5z-2=3

Solution for 11z-1/5z-2=3 equation:

11z-1/5z-2=3

We move all terms to the left:

11z-1/5z-2-(3)=0


Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R


We add all the numbers together, and all the variables

11z-1/5z-5=0

We multiply all the terms by the denominator


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

Wy multiply elements

55z^2-25z-1=0

a = 55; b = -25; c = -1;
Δ = b2-4ac
Δ = -252-4·55·(-1)
Δ = 845
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:

$\sqrt{\Delta}=\sqrt{845}=\sqrt{169*5}=\sqrt{169}*\sqrt{5}=13\sqrt{5}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-13\sqrt{5}}{2*55}=\frac{25-13\sqrt{5}}{110}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+13\sqrt{5}}{2*55}=\frac{25+13\sqrt{5}}{110}
$