331=-q^2-2q+526

Solution for 331=-q^2-2q+526 equation:

331=-q^2-2q+526

We move all terms to the left:

331-(-q^2-2q+526)=0

We get rid of parentheses

q^2+2q-526+331=0

We add all the numbers together, and all the variables

q^2+2q-195=0

a = 1; b = 2; c = -195;
Δ = b2-4ac
Δ = 22-4·1·(-195)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-28}{2*1}=\frac{-30}{2}
=-15
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+28}{2*1}=\frac{26}{2}
=13
$