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

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

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

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=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+30x-1=0

a = -6; b = 30; c = -1;
Δ = b2-4ac
Δ = 302-4·(-6)·(-1)
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{219}}{2*-6}=\frac{-30-2\sqrt{219}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{219}}{2*-6}=\frac{-30+2\sqrt{219}}{-12}
$