33=x(2x+8)

Solution for 33=x(2x+8) equation:

33=x(2x+8)

We move all terms to the left:

33-(x(2x+8))=0


We calculate terms in parentheses: -(x(2x+8)), so:

x(2x+8)

We multiply parentheses

2x^2+8x

Back to the equation:

-(2x^2+8x)


We get rid of parentheses

-2x^2-8x+33=0

a = -2; b = -8; c = +33;
Δ = b2-4ac
Δ = -82-4·(-2)·33
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{-(-8)-2\sqrt{82}}{2*-2}=\frac{8-2\sqrt{82}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{82}}{2*-2}=\frac{8+2\sqrt{82}}{-4}
$