X-1/4x=675

Solution for X-1/4x=675 equation:

X-1/4X=675

We move all terms to the left:

X-1/4X-(675)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We multiply all the terms by the denominator


X*4X-675*4X-1=0

Wy multiply elements

4X^2-2700X-1=0

a = 4; b = -2700; c = -1;
Δ = b2-4ac
Δ = -27002-4·4·(-1)
Δ = 7290016
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:

$\sqrt{\Delta}=\sqrt{7290016}=\sqrt{16*455626}=\sqrt{16}*\sqrt{455626}=4\sqrt{455626}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2700)-4\sqrt{455626}}{2*4}=\frac{2700-4\sqrt{455626}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2700)+4\sqrt{455626}}{2*4}=\frac{2700+4\sqrt{455626}}{8}
$