11+2x=3(x2)

Solution for 11+2x=3(x2) equation:

11+2x=3(x2)

We move all terms to the left:

11+2x-(3(x2))=0

determiningTheFunctionDomain
2x-3x2+11=0

We add all the numbers together, and all the variables

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

a = -3; b = 2; c = +11;
Δ = b2-4ac
Δ = 22-4·(-3)·11
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{34}}{2*-3}=\frac{-2-2\sqrt{34}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{34}}{2*-3}=\frac{-2+2\sqrt{34}}{-6}
$