X-1/4x=75

Solution for X-1/4x=75 equation:

X-1/4X=75

We move all terms to the left:

X-1/4X-(75)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-75*4X-1=0

Wy multiply elements

4X^2-300X-1=0

a = 4; b = -300; c = -1;
Δ = b2-4ac
Δ = -3002-4·4·(-1)
Δ = 90016
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:

$\sqrt{\Delta}=\sqrt{90016}=\sqrt{16*5626}=\sqrt{16}*\sqrt{5626}=4\sqrt{5626}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-4\sqrt{5626}}{2*4}=\frac{300-4\sqrt{5626}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+4\sqrt{5626}}{2*4}=\frac{300+4\sqrt{5626}}{8}
$