27-6x=7/4x

Solution for 27-6x=7/4x equation:

27-6x=7/4x

We move all terms to the left:

27-6x-(7/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-6x-(+7/4x)+27=0

We get rid of parentheses

-6x-7/4x+27=0

We multiply all the terms by the denominator


-6x*4x+27*4x-7=0

Wy multiply elements

-24x^2+108x-7=0

a = -24; b = 108; c = -7;
Δ = b2-4ac
Δ = 1082-4·(-24)·(-7)
Δ = 10992
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:

$\sqrt{\Delta}=\sqrt{10992}=\sqrt{16*687}=\sqrt{16}*\sqrt{687}=4\sqrt{687}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-4\sqrt{687}}{2*-24}=\frac{-108-4\sqrt{687}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+4\sqrt{687}}{2*-24}=\frac{-108+4\sqrt{687}}{-48}
$