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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

2x^2+4x-(+3x+11/2)=0

We get rid of parentheses

2x^2+4x-3x-11/2=0

We multiply all the terms by the denominator


2x^2*2+4x*2-3x*2-11=0

Wy multiply elements

4x^2+8x-6x-11=0

We add all the numbers together, and all the variables

4x^2+2x-11=0

a = 4; b = 2; c = -11;
Δ = b2-4ac
Δ = 22-4·4·(-11)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{5}}{2*4}=\frac{-2-6\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{5}}{2*4}=\frac{-2+6\sqrt{5}}{8}
$