-4/3x-8=-1/4x+5

Solution for -4/3x-8=-1/4x+5 equation:

-4/3x-8=-1/4x+5

We move all terms to the left:

-4/3x-8-(-1/4x+5)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

-4/3x+1/4x-5-8=0

We calculate fractions


(-16x)/12x^2+3x/12x^2-5-8=0

We add all the numbers together, and all the variables

(-16x)/12x^2+3x/12x^2-13=0

We multiply all the terms by the denominator


(-16x)+3x-13*12x^2=0

We add all the numbers together, and all the variables

3x+(-16x)-13*12x^2=0

Wy multiply elements

-156x^2+3x+(-16x)=0

We get rid of parentheses

-156x^2+3x-16x=0

We add all the numbers together, and all the variables

-156x^2-13x=0

a = -156; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·(-156)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*-156}=\frac{0}{-312}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*-156}=\frac{26}{-312}
=-1/12
$