x/8x-6x+4+5=19

Solution for x/8x-6x+4+5=19 equation:

x/8x-6x+4+5=19

We move all terms to the left:

x/8x-6x+4+5-(19)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-6x+x/8x-10=0

We multiply all the terms by the denominator


-6x*8x+x-10*8x=0

We add all the numbers together, and all the variables

x-6x*8x-10*8x=0

Wy multiply elements

-48x^2+x-80x=0

We add all the numbers together, and all the variables

-48x^2-79x=0

a = -48; b = -79; c = 0;
Δ = b2-4ac
Δ = -792-4·(-48)·0
Δ = 6241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6241}=79$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-79)-79}{2*-48}=\frac{0}{-96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-79)+79}{2*-48}=\frac{158}{-96}
=-1+31/48
$