x(3x+6)=8(x+22)

Solution for x(3x+6)=8(x+22) equation:

x(3x+6)=8(x+22)

We move all terms to the left:

x(3x+6)-(8(x+22))=0

We multiply parentheses

3x^2+6x-(8(x+22))=0


We calculate terms in parentheses: -(8(x+22)), so:

8(x+22)

We multiply parentheses

8x+176

Back to the equation:

-(8x+176)


We get rid of parentheses

3x^2+6x-8x-176=0

We add all the numbers together, and all the variables

3x^2-2x-176=0

a = 3; b = -2; c = -176;
Δ = b2-4ac
Δ = -22-4·3·(-176)
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-46}{2*3}=\frac{-44}{6}
=-7+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+46}{2*3}=\frac{48}{6}
=8
$