-1/4x-4=7/6x-3

Solution for -1/4x-4=7/6x-3 equation:

-1/4x-4=7/6x-3

We move all terms to the left:

-1/4x-4-(7/6x-3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 6x-3)!=0

x∈R


We get rid of parentheses

-1/4x-7/6x+3-4=0

We calculate fractions


(-6x)/24x^2+(-28x)/24x^2+3-4=0

We add all the numbers together, and all the variables

(-6x)/24x^2+(-28x)/24x^2-1=0

We multiply all the terms by the denominator


(-6x)+(-28x)-1*24x^2=0

Wy multiply elements

-24x^2+(-6x)+(-28x)=0

We get rid of parentheses

-24x^2-6x-28x=0

We add all the numbers together, and all the variables

-24x^2-34x=0

a = -24; b = -34; c = 0;
Δ = b2-4ac
Δ = -342-4·(-24)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-34}{2*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+34}{2*-24}=\frac{68}{-48}
=-1+5/12
$