8+21/4x=-7/4x-2x

Solution for 8+21/4x=-7/4x-2x equation:

8+21/4x=-7/4x-2x

We move all terms to the left:

8+21/4x-(-7/4x-2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 4x-2x)!=0

x∈R


We add all the numbers together, and all the variables

21/4x-(-2x-7/4x)+8=0

We get rid of parentheses

21/4x+2x+7/4x+8=0

We multiply all the terms by the denominator


2x*4x+8*4x+21+7=0

We add all the numbers together, and all the variables

2x*4x+8*4x+28=0

Wy multiply elements

8x^2+32x+28=0

a = 8; b = 32; c = +28;
Δ = b2-4ac
Δ = 322-4·8·28
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8\sqrt{2}}{2*8}=\frac{-32-8\sqrt{2}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8\sqrt{2}}{2*8}=\frac{-32+8\sqrt{2}}{16}
$