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

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

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

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

-3x-(1/4x-4)+11=0

We get rid of parentheses

-3x-1/4x+4+11=0

We multiply all the terms by the denominator


-3x*4x+4*4x+11*4x-1=0

Wy multiply elements

-12x^2+16x+44x-1=0

We add all the numbers together, and all the variables

-12x^2+60x-1=0

a = -12; b = 60; c = -1;
Δ = b2-4ac
Δ = 602-4·(-12)·(-1)
Δ = 3552
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:

$\sqrt{\Delta}=\sqrt{3552}=\sqrt{16*222}=\sqrt{16}*\sqrt{222}=4\sqrt{222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{222}}{2*-12}=\frac{-60-4\sqrt{222}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{222}}{2*-12}=\frac{-60+4\sqrt{222}}{-24}
$