X=1/4y-1

Solution for X=1/4y-1 equation:

X=1/4X-1

We move all terms to the left:

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


Domain of the equation: 4X-1)!=0

X∈R


We get rid of parentheses

X-1/4X+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

4X^2+4X-1=0

a = 4; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·4·(-1)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*4}=\frac{-4-4\sqrt{2}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*4}=\frac{-4+4\sqrt{2}}{8}
$