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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

x(x+11)

We multiply parentheses

x^2+11x

Back to the equation:

-(x^2+11x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-8x+3=0

a = -1; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·(-1)·3
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{19}}{2*-1}=\frac{8-2\sqrt{19}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{19}}{2*-1}=\frac{8+2\sqrt{19}}{-2}
$