2x(3+4x)=11

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

2x(3+4x)=11

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

8x^2+6x-11=0

a = 8; b = 6; c = -11;
Δ = b2-4ac
Δ = 62-4·8·(-11)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{97}}{2*8}=\frac{-6-2\sqrt{97}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{97}}{2*8}=\frac{-6+2\sqrt{97}}{16}
$