w(2w+7)=99

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

w(2w+7)=99

We move all terms to the left:

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

We multiply parentheses

2w^2+7w-99=0

a = 2; b = 7; c = -99;
Δ = b2-4ac
Δ = 72-4·2·(-99)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-29}{2*2}=\frac{-36}{4}
=-9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+29}{2*2}=\frac{22}{4}
=5+1/2
$