1/4x=x-27

Solution for 1/4x=x-27 equation:

1/4x=x-27

We move all terms to the left:

1/4x-(x-27)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-x+27=0

We multiply all the terms by the denominator


-x*4x+27*4x+1=0

Wy multiply elements

-4x^2+108x+1=0

a = -4; b = 108; c = +1;
Δ = b2-4ac
Δ = 1082-4·(-4)·1
Δ = 11680
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:

$\sqrt{\Delta}=\sqrt{11680}=\sqrt{16*730}=\sqrt{16}*\sqrt{730}=4\sqrt{730}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-4\sqrt{730}}{2*-4}=\frac{-108-4\sqrt{730}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+4\sqrt{730}}{2*-4}=\frac{-108+4\sqrt{730}}{-8}
$