1/4x=x+150

Solution for 1/4x=x+150 equation:

1/4x=x+150

We move all terms to the left:

1/4x-(x+150)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-x-150=0

We multiply all the terms by the denominator


-x*4x-150*4x+1=0

Wy multiply elements

-4x^2-600x+1=0

a = -4; b = -600; c = +1;
Δ = b2-4ac
Δ = -6002-4·(-4)·1
Δ = 360016
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:

$\sqrt{\Delta}=\sqrt{360016}=\sqrt{16*22501}=\sqrt{16}*\sqrt{22501}=4\sqrt{22501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-600)-4\sqrt{22501}}{2*-4}=\frac{600-4\sqrt{22501}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-600)+4\sqrt{22501}}{2*-4}=\frac{600+4\sqrt{22501}}{-8}
$