99=(w+7)(2w)

Solution for 99=(w+7)(2w) equation:

99=(w+7)(2w)

We move all terms to the left:

99-((w+7)(2w))=0


We calculate terms in parentheses: -((w+7)2w), so:

(w+7)2w

We multiply parentheses

2w^2+14w

Back to the equation:

-(2w^2+14w)


We get rid of parentheses

-2w^2-14w+99=0

a = -2; b = -14; c = +99;
Δ = b2-4ac
Δ = -142-4·(-2)·99
Δ = 988
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:

$\sqrt{\Delta}=\sqrt{988}=\sqrt{4*247}=\sqrt{4}*\sqrt{247}=2\sqrt{247}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{247}}{2*-2}=\frac{14-2\sqrt{247}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{247}}{2*-2}=\frac{14+2\sqrt{247}}{-4}
$