3(x+1)=2x(x+11)

Solution for 3(x+1)=2x(x+11) equation:

3(x+1)=2x(x+11)

We move all terms to the left:

3(x+1)-(2x(x+11))=0

We multiply parentheses

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


We calculate terms in parentheses: -(2x(x+11)), so:

2x(x+11)

We multiply parentheses

2x^2+22x

Back to the equation:

-(2x^2+22x)


We get rid of parentheses

-2x^2+3x-22x+3=0

We add all the numbers together, and all the variables

-2x^2-19x+3=0

a = -2; b = -19; c = +3;
Δ = b2-4ac
Δ = -192-4·(-2)·3
Δ = 385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{385}}{2*-2}=\frac{19-\sqrt{385}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{385}}{2*-2}=\frac{19+\sqrt{385}}{-4}
$