-2/7z=2z+20

Solution for -2/7z=2z+20 equation:

-2/7z=2z+20

We move all terms to the left:

-2/7z-(2z+20)=0


Domain of the equation: 7z!=0

z!=0/7

z!=0

z∈R


We get rid of parentheses

-2/7z-2z-20=0

We multiply all the terms by the denominator


-2z*7z-20*7z-2=0

Wy multiply elements

-14z^2-140z-2=0

a = -14; b = -140; c = -2;
Δ = b2-4ac
Δ = -1402-4·(-14)·(-2)
Δ = 19488
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:

$\sqrt{\Delta}=\sqrt{19488}=\sqrt{16*1218}=\sqrt{16}*\sqrt{1218}=4\sqrt{1218}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-4\sqrt{1218}}{2*-14}=\frac{140-4\sqrt{1218}}{-28}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+4\sqrt{1218}}{2*-14}=\frac{140+4\sqrt{1218}}{-28}
$