x=36/2x+3

Solution for x=36/2x+3 equation:

x=36/2x+3

We move all terms to the left:

x-(36/2x+3)=0


Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

x-36/2x-3=0

We multiply all the terms by the denominator


x*2x-3*2x-36=0

Wy multiply elements

2x^2-6x-36=0

a = 2; b = -6; c = -36;
Δ = b2-4ac
Δ = -62-4·2·(-36)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*2}=\frac{24}{4}
=6
$