3/7z+z=180

Solution for 3/7z+z=180 equation:

3/7z+z=180

We move all terms to the left:

3/7z+z-(180)=0


Domain of the equation: 7z!=0

z!=0/7

z!=0

z∈R


We add all the numbers together, and all the variables

z+3/7z-180=0

We multiply all the terms by the denominator


z*7z-180*7z+3=0

Wy multiply elements

7z^2-1260z+3=0

a = 7; b = -1260; c = +3;
Δ = b2-4ac
Δ = -12602-4·7·3
Δ = 1587516
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:

$\sqrt{\Delta}=\sqrt{1587516}=\sqrt{4*396879}=\sqrt{4}*\sqrt{396879}=2\sqrt{396879}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1260)-2\sqrt{396879}}{2*7}=\frac{1260-2\sqrt{396879}}{14}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1260)+2\sqrt{396879}}{2*7}=\frac{1260+2\sqrt{396879}}{14}
$