z^2/12+z=4

Solution for z^2/12+z=4 equation:

z^2/12+z=4

We move all terms to the left:

z^2/12+z-(4)=0

We multiply all the terms by the denominator


z^2+z*12-4*12=0

We add all the numbers together, and all the variables

z^2+z*12-48=0

Wy multiply elements

z^2+12z-48=0

a = 1; b = 12; c = -48;
Δ = b2-4ac
Δ = 122-4·1·(-48)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{21}}{2*1}=\frac{-12-4\sqrt{21}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{21}}{2*1}=\frac{-12+4\sqrt{21}}{2}
$