2x(4+3x)=9+11x

Solution for 2x(4+3x)=9+11x equation:

2x(4+3x)=9+11x

We move all terms to the left:

2x(4+3x)-(9+11x)=0

We add all the numbers together, and all the variables

2x(3x+4)-(11x+9)=0

We multiply parentheses

6x^2+8x-(11x+9)=0

We get rid of parentheses

6x^2+8x-11x-9=0

We add all the numbers together, and all the variables

6x^2-3x-9=0

a = 6; b = -3; c = -9;
Δ = b2-4ac
Δ = -32-4·6·(-9)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-15}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+15}{2*6}=\frac{18}{12}
=1+1/2
$