x=11/2x+3

Solution for x=11/2x+3 equation:

x=11/2x+3

We move all terms to the left:

x-(11/2x+3)=0


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

x∈R


We get rid of parentheses

x-11/2x-3=0

We multiply all the terms by the denominator


x*2x-3*2x-11=0

Wy multiply elements

2x^2-6x-11=0

a = 2; b = -6; c = -11;
Δ = b2-4ac
Δ = -62-4·2·(-11)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{31}}{2*2}=\frac{6-2\sqrt{31}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{31}}{2*2}=\frac{6+2\sqrt{31}}{4}
$