X+1/4x=300

Solution for X+1/4x=300 equation:

X+1/4X=300

We move all terms to the left:

X+1/4X-(300)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-300*4X+1=0

Wy multiply elements

4X^2-1200X+1=0

a = 4; b = -1200; c = +1;
Δ = b2-4ac
Δ = -12002-4·4·1
Δ = 1439984
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:

$\sqrt{\Delta}=\sqrt{1439984}=\sqrt{16*89999}=\sqrt{16}*\sqrt{89999}=4\sqrt{89999}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1200)-4\sqrt{89999}}{2*4}=\frac{1200-4\sqrt{89999}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1200)+4\sqrt{89999}}{2*4}=\frac{1200+4\sqrt{89999}}{8}
$