685=4q2+156

Solution for 685=4q2+156 equation:

685=4q^2+156

We move all terms to the left:

685-(4q^2+156)=0

We get rid of parentheses

-4q^2-156+685=0

We add all the numbers together, and all the variables

-4q^2+529=0

a = -4; b = 0; c = +529;
Δ = b2-4ac
Δ = 02-4·(-4)·529
Δ = 8464
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8464}=92$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-92}{2*-4}=\frac{-92}{-8}
=11+1/2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+92}{2*-4}=\frac{92}{-8}
=-11+1/2
$