5z-11/3z+7=-2

Solution for 5z-11/3z+7=-2 equation:

5z-11/3z+7=-2

We move all terms to the left:

5z-11/3z+7-(-2)=0


Domain of the equation: 3z!=0

z!=0/3

z!=0

z∈R


We add all the numbers together, and all the variables

5z-11/3z+9=0

We multiply all the terms by the denominator


5z*3z+9*3z-11=0

Wy multiply elements

15z^2+27z-11=0

a = 15; b = 27; c = -11;
Δ = b2-4ac
Δ = 272-4·15·(-11)
Δ = 1389
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{-(27)-\sqrt{1389}}{2*15}=\frac{-27-\sqrt{1389}}{30}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{1389}}{2*15}=\frac{-27+\sqrt{1389}}{30}
$