1/4x=x-18

Solution for 1/4x=x-18 equation:

1/4x=x-18

We move all terms to the left:

1/4x-(x-18)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-x+18=0

We multiply all the terms by the denominator


-x*4x+18*4x+1=0

Wy multiply elements

-4x^2+72x+1=0

a = -4; b = 72; c = +1;
Δ = b2-4ac
Δ = 722-4·(-4)·1
Δ = 5200
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:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-20\sqrt{13}}{2*-4}=\frac{-72-20\sqrt{13}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+20\sqrt{13}}{2*-4}=\frac{-72+20\sqrt{13}}{-8}
$