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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(3x(x-4)), so:

3x(x-4)

We multiply parentheses

3x^2-12x

Back to the equation:

-(3x^2-12x)


We get rid of parentheses

-3x^2+2x+12x+11=0

We add all the numbers together, and all the variables

-3x^2+14x+11=0

a = -3; b = 14; c = +11;
Δ = b2-4ac
Δ = 142-4·(-3)·11
Δ = 328
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:

$\sqrt{\Delta}=\sqrt{328}=\sqrt{4*82}=\sqrt{4}*\sqrt{82}=2\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{82}}{2*-3}=\frac{-14-2\sqrt{82}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{82}}{2*-3}=\frac{-14+2\sqrt{82}}{-6}
$