X/4x-2x=7

Solution for X/4x-2x=7 equation:

X/4X-2X=7

We move all terms to the left:

X/4X-2X-(7)=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+X/4X-7=0

We multiply all the terms by the denominator


-2X*4X+X-7*4X=0

We add all the numbers together, and all the variables

X-2X*4X-7*4X=0

Wy multiply elements

-8X^2+X-28X=0

We add all the numbers together, and all the variables

-8X^2-27X=0

a = -8; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-8)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*-8}=\frac{0}{-16}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-8}=\frac{54}{-16}
=-3+3/8
$