2x(2+3x)=11(8+x)

Solution for 2x(2+3x)=11(8+x) equation:

2x(2+3x)=11(8+x)

We move all terms to the left:

2x(2+3x)-(11(8+x))=0

We add all the numbers together, and all the variables

2x(3x+2)-(11(x+8))=0

We multiply parentheses

6x^2+4x-(11(x+8))=0


We calculate terms in parentheses: -(11(x+8)), so:

11(x+8)

We multiply parentheses

11x+88

Back to the equation:

-(11x+88)


We get rid of parentheses

6x^2+4x-11x-88=0

We add all the numbers together, and all the variables

6x^2-7x-88=0

a = 6; b = -7; c = -88;
Δ = b2-4ac
Δ = -72-4·6·(-88)
Δ = 2161
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{-(-7)-\sqrt{2161}}{2*6}=\frac{7-\sqrt{2161}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{2161}}{2*6}=\frac{7+\sqrt{2161}}{12}
$