228=(2w+6)(w)

Solution for 228=(2w+6)(w) equation:

228=(2w+6)(w)

We move all terms to the left:

228-((2w+6)(w))=0


We calculate terms in parentheses: -((2w+6)w), so:

(2w+6)w

We multiply parentheses

2w^2+6w

Back to the equation:

-(2w^2+6w)


We get rid of parentheses

-2w^2-6w+228=0

a = -2; b = -6; c = +228;
Δ = b2-4ac
Δ = -62-4·(-2)·228
Δ = 1860
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1860}=\sqrt{4*465}=\sqrt{4}*\sqrt{465}=2\sqrt{465}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{465}}{2*-2}=\frac{6-2\sqrt{465}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{465}}{2*-2}=\frac{6+2\sqrt{465}}{-4}
$