14/7z=9z+34

Solution for 14/7z=9z+34 equation:

14/7z=9z+34

We move all terms to the left:

14/7z-(9z+34)=0


Domain of the equation: 7z!=0

z!=0/7

z!=0

z∈R


We get rid of parentheses

14/7z-9z-34=0

We multiply all the terms by the denominator


-9z*7z-34*7z+14=0

Wy multiply elements

-63z^2-238z+14=0

a = -63; b = -238; c = +14;
Δ = b2-4ac
Δ = -2382-4·(-63)·14
Δ = 60172
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:

$\sqrt{\Delta}=\sqrt{60172}=\sqrt{196*307}=\sqrt{196}*\sqrt{307}=14\sqrt{307}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-238)-14\sqrt{307}}{2*-63}=\frac{238-14\sqrt{307}}{-126}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-238)+14\sqrt{307}}{2*-63}=\frac{238+14\sqrt{307}}{-126}
$