7z-5/2z=3

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

7z-5/2z=3

We move all terms to the left:

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


Domain of the equation: 2z!=0

z!=0/2

z!=0

z∈R


We multiply all the terms by the denominator


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

Wy multiply elements

14z^2-6z-5=0

a = 14; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·14·(-5)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{79}}{2*14}=\frac{6-2\sqrt{79}}{28}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{79}}{2*14}=\frac{6+2\sqrt{79}}{28}
$