5z-7/3z=2

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

5z-7/3z=2

We move all terms to the left:

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


Domain of the equation: 3z!=0

z!=0/3

z!=0

z∈R


We multiply all the terms by the denominator


5z*3z-2*3z-7=0

Wy multiply elements

15z^2-6z-7=0

a = 15; b = -6; c = -7;
Δ = b2-4ac
Δ = -62-4·15·(-7)
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{114}}{2*15}=\frac{6-2\sqrt{114}}{30}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{114}}{2*15}=\frac{6+2\sqrt{114}}{30}
$