36q^2-59=0

Solution for 36q^2-59=0 equation:

36q^2-59=0

a = 36; b = 0; c = -59;
Δ = b2-4ac
Δ = 02-4·36·(-59)
Δ = 8496
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:

$\sqrt{\Delta}=\sqrt{8496}=\sqrt{144*59}=\sqrt{144}*\sqrt{59}=12\sqrt{59}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{59}}{2*36}=\frac{0-12\sqrt{59}}{72}
=-\frac{12\sqrt{59}}{72}
=-\frac{\sqrt{59}}{6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{59}}{2*36}=\frac{0+12\sqrt{59}}{72}
=\frac{12\sqrt{59}}{72}
=\frac{\sqrt{59}}{6}
$