2(1/4x-7)=4+1/3x

Solution for 2(1/4x-7)=4+1/3x equation:

2(1/4x-7)=4+1/3x

We move all terms to the left:

2(1/4x-7)-(4+1/3x)=0


Domain of the equation: 4x-7)!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2(1/4x-7)-(1/3x+4)=0

We multiply parentheses

2x-(1/3x+4)-14=0

We get rid of parentheses

2x-1/3x-4-14=0

We multiply all the terms by the denominator


2x*3x-4*3x-14*3x-1=0

Wy multiply elements

6x^2-12x-42x-1=0

We add all the numbers together, and all the variables

6x^2-54x-1=0

a = 6; b = -54; c = -1;
Δ = b2-4ac
Δ = -542-4·6·(-1)
Δ = 2940
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-14\sqrt{15}}{2*6}=\frac{54-14\sqrt{15}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+14\sqrt{15}}{2*6}=\frac{54+14\sqrt{15}}{12}
$