X=4+9/2y

Solution for X=4+9/2y equation:

X=4+9/2X

We move all terms to the left:

X-(4+9/2X)=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-(9/2X+4)=0

We get rid of parentheses

X-9/2X-4=0

We multiply all the terms by the denominator


X*2X-4*2X-9=0

Wy multiply elements

2X^2-8X-9=0

a = 2; b = -8; c = -9;
Δ = b2-4ac
Δ = -82-4·2·(-9)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{34}}{2*2}=\frac{8-2\sqrt{34}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{34}}{2*2}=\frac{8+2\sqrt{34}}{4}
$