x/8x+5=6x-15

Solution for x/8x+5=6x-15 equation:

x/8x+5=6x-15

We move all terms to the left:

x/8x+5-(6x-15)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

x/8x-6x+15+5=0

We multiply all the terms by the denominator


x-6x*8x+15*8x+5*8x=0

Wy multiply elements

-48x^2+x+120x+40x=0

We add all the numbers together, and all the variables

-48x^2+161x=0

a = -48; b = 161; c = 0;
Δ = b2-4ac
Δ = 1612-4·(-48)·0
Δ = 25921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25921}=161$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(161)-161}{2*-48}=\frac{-322}{-96}
=3+17/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(161)+161}{2*-48}=\frac{0}{-96}
=0
$