6z=4/12z-8

Solution for 6z=4/12z-8 equation:

6z=4/12z-8

We move all terms to the left:

6z-(4/12z-8)=0


Domain of the equation: 12z-8)!=0

z∈R


We get rid of parentheses

6z-4/12z+8=0

We multiply all the terms by the denominator


6z*12z+8*12z-4=0

Wy multiply elements

72z^2+96z-4=0

a = 72; b = 96; c = -4;
Δ = b2-4ac
Δ = 962-4·72·(-4)
Δ = 10368
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:

$\sqrt{\Delta}=\sqrt{10368}=\sqrt{5184*2}=\sqrt{5184}*\sqrt{2}=72\sqrt{2}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-72\sqrt{2}}{2*72}=\frac{-96-72\sqrt{2}}{144}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+72\sqrt{2}}{2*72}=\frac{-96+72\sqrt{2}}{144}
$