-1/4x-7+9/4x+2x=4

Solution for -1/4x-7+9/4x+2x=4 equation:

-1/4x-7+9/4x+2x=4

We move all terms to the left:

-1/4x-7+9/4x+2x-(4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x-1/4x+9/4x-11=0

We multiply all the terms by the denominator


2x*4x-11*4x-1+9=0

We add all the numbers together, and all the variables

2x*4x-11*4x+8=0

Wy multiply elements

8x^2-44x+8=0

a = 8; b = -44; c = +8;
Δ = b2-4ac
Δ = -442-4·8·8
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{105}}{2*8}=\frac{44-4\sqrt{105}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{105}}{2*8}=\frac{44+4\sqrt{105}}{16}
$