Z/2z-8=5z+7

Solution for Z/2z-8=5z+7 equation:

/2Z-8=5Z+7

We move all terms to the left:

/2Z-8-(5Z+7)=0


Domain of the equation: 2Z!=0

Z!=0/2

Z!=0

Z∈R


We get rid of parentheses

/2Z-5Z-7-8=0

We multiply all the terms by the denominator


-5Z*2Z-7*2Z-8*2Z+=0

We add all the numbers together, and all the variables

-5Z*2Z-7*2Z-8*2Z=0

Wy multiply elements

-10Z^2-14Z-16Z=0

We add all the numbers together, and all the variables

-10Z^2-30Z=0

a = -10; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·(-10)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$Z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*-10}=\frac{0}{-20}
=0
$
$Z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*-10}=\frac{60}{-20}
=-3
$