2x(11+3x/2)+3=7

Solution for 2x(11+3x/2)+3=7 equation:

2x(11+3x/2)+3=7

We move all terms to the left:

2x(11+3x/2)+3-(7)=0

We add all the numbers together, and all the variables

2x(3x/2+11)+3-7=0

We add all the numbers together, and all the variables

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

We multiply parentheses

6x^2+22x-4=0

a = 6; b = 22; c = -4;
Δ = b2-4ac
Δ = 222-4·6·(-4)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{145}}{2*6}=\frac{-22-2\sqrt{145}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{145}}{2*6}=\frac{-22+2\sqrt{145}}{12}
$