2q(q+2)=176

Solution for 2q(q+2)=176 equation:

2q(q+2)=176

We move all terms to the left:

2q(q+2)-(176)=0

We multiply parentheses

2q^2+4q-176=0

a = 2; b = 4; c = -176;
Δ = b2-4ac
Δ = 42-4·2·(-176)
Δ = 1424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1424}=\sqrt{16*89}=\sqrt{16}*\sqrt{89}=4\sqrt{89}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{89}}{2*2}=\frac{-4-4\sqrt{89}}{4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{89}}{2*2}=\frac{-4+4\sqrt{89}}{4}
$