X=2y+5/4y+5

Solution for X=2y+5/4y+5 equation:

X=2X+5/4X+5

We move all terms to the left:

X-(2X+5/4X+5)=0


Domain of the equation: 4X+5)!=0

X∈R


We get rid of parentheses

X-2X-5/4X-5=0

We multiply all the terms by the denominator


X*4X-2X*4X-5*4X-5=0

Wy multiply elements

4X^2-8X^2-20X-5=0

We add all the numbers together, and all the variables

-4X^2-20X-5=0

a = -4; b = -20; c = -5;
Δ = b2-4ac
Δ = -202-4·(-4)·(-5)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{5}}{2*-4}=\frac{20-8\sqrt{5}}{-8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{5}}{2*-4}=\frac{20+8\sqrt{5}}{-8}
$