X-3-1/4x=30

Solution for X-3-1/4x=30 equation:

X-3-1/4X=30

We move all terms to the left:

X-3-1/4X-(30)=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-33=0

We multiply all the terms by the denominator


X*4X-33*4X-1=0

Wy multiply elements

4X^2-132X-1=0

a = 4; b = -132; c = -1;
Δ = b2-4ac
Δ = -1322-4·4·(-1)
Δ = 17440
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:

$\sqrt{\Delta}=\sqrt{17440}=\sqrt{16*1090}=\sqrt{16}*\sqrt{1090}=4\sqrt{1090}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-4\sqrt{1090}}{2*4}=\frac{132-4\sqrt{1090}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+4\sqrt{1090}}{2*4}=\frac{132+4\sqrt{1090}}{8}
$