/8x-5=5x+13*

Solution for /8x-5=5x+13* equation:

/8x-5=5x+13*

We move all terms to the left:

/8x-5-(5x+13*)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

/8x-(+5x)-5=0

We get rid of parentheses

/8x-5x-5=0

We multiply all the terms by the denominator


-5x*8x-5*8x+=0

We add all the numbers together, and all the variables

-5x*8x-5*8x=0

Wy multiply elements

-40x^2-40x=0

a = -40; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·(-40)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*-40}=\frac{0}{-80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*-40}=\frac{80}{-80}
=-1
$