X-1/4x=67.5

Solution for X-1/4x=67.5 equation:

X-1/4X=67.5

We move all terms to the left:

X-1/4X-(67.5)=0


Domain of the equation: 4X!=0

X!=0/4

X!=0

X∈R


We add all the numbers together, and all the variables

X-1/4X-67.5=0

We multiply all the terms by the denominator


X*4X-(67.5)*4X-1=0

We multiply parentheses

X*4X-270X-1=0

Wy multiply elements

4X^2-270X-1=0

a = 4; b = -270; c = -1;
Δ = b2-4ac
Δ = -2702-4·4·(-1)
Δ = 72916
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:

$\sqrt{\Delta}=\sqrt{72916}=\sqrt{4*18229}=\sqrt{4}*\sqrt{18229}=2\sqrt{18229}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-270)-2\sqrt{18229}}{2*4}=\frac{270-2\sqrt{18229}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-270)+2\sqrt{18229}}{2*4}=\frac{270+2\sqrt{18229}}{8}
$