-7z+180/6z+60=0

Solution for -7z+180/6z+60=0 equation:

-7z+180/6z+60=0


Domain of the equation: 6z!=0

z!=0/6

z!=0

z∈R


We multiply all the terms by the denominator


-7z*6z+60*6z+180=0

Wy multiply elements

-42z^2+360z+180=0

a = -42; b = 360; c = +180;
Δ = b2-4ac
Δ = 3602-4·(-42)·180
Δ = 159840
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:

$\sqrt{\Delta}=\sqrt{159840}=\sqrt{144*1110}=\sqrt{144}*\sqrt{1110}=12\sqrt{1110}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-12\sqrt{1110}}{2*-42}=\frac{-360-12\sqrt{1110}}{-84}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+12\sqrt{1110}}{2*-42}=\frac{-360+12\sqrt{1110}}{-84}
$