-4/3x+8=1/4x-1

Solution for -4/3x+8=1/4x-1 equation:

-4/3x+8=1/4x-1

We move all terms to the left:

-4/3x+8-(1/4x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-1)!=0

x∈R


We get rid of parentheses

-4/3x-1/4x+1+8=0

We calculate fractions


(-16x)/12x^2+(-3x)/12x^2+1+8=0

We add all the numbers together, and all the variables

(-16x)/12x^2+(-3x)/12x^2+9=0

We multiply all the terms by the denominator


(-16x)+(-3x)+9*12x^2=0

Wy multiply elements

108x^2+(-16x)+(-3x)=0

We get rid of parentheses

108x^2-16x-3x=0

We add all the numbers together, and all the variables

108x^2-19x=0

a = 108; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·108·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*108}=\frac{0}{216}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*108}=\frac{38}{216}
=19/108
$