X=5+11/2y

Solution for X=5+11/2y equation:

X=5+11/2X

We move all terms to the left:

X-(5+11/2X)=0


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(11/2X+5)=0

We get rid of parentheses

X-11/2X-5=0

We multiply all the terms by the denominator


X*2X-5*2X-11=0

Wy multiply elements

2X^2-10X-11=0

a = 2; b = -10; c = -11;
Δ = b2-4ac
Δ = -102-4·2·(-11)
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{47}}{2*2}=\frac{10-2\sqrt{47}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{47}}{2*2}=\frac{10+2\sqrt{47}}{4}
$