1/5z-8=8z-47

Solution for 1/5z-8=8z-47 equation:

1/5z-8=8z-47

We move all terms to the left:

1/5z-8-(8z-47)=0


Domain of the equation: 5z!=0

z!=0/5

z!=0

z∈R


We get rid of parentheses

1/5z-8z+47-8=0

We multiply all the terms by the denominator


-8z*5z+47*5z-8*5z+1=0

Wy multiply elements

-40z^2+235z-40z+1=0

We add all the numbers together, and all the variables

-40z^2+195z+1=0

a = -40; b = 195; c = +1;
Δ = b2-4ac
Δ = 1952-4·(-40)·1
Δ = 38185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(195)-\sqrt{38185}}{2*-40}=\frac{-195-\sqrt{38185}}{-80}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(195)+\sqrt{38185}}{2*-40}=\frac{-195+\sqrt{38185}}{-80}
$