9q^2-35=144

Solution for 9q^2-35=144 equation:

9q^2-35=144

We move all terms to the left:

9q^2-35-(144)=0

We add all the numbers together, and all the variables

9q^2-179=0

a = 9; b = 0; c = -179;
Δ = b2-4ac
Δ = 02-4·9·(-179)
Δ = 6444
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:

$\sqrt{\Delta}=\sqrt{6444}=\sqrt{36*179}=\sqrt{36}*\sqrt{179}=6\sqrt{179}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{179}}{2*9}=\frac{0-6\sqrt{179}}{18}
=-\frac{6\sqrt{179}}{18}
=-\frac{\sqrt{179}}{3}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{179}}{2*9}=\frac{0+6\sqrt{179}}{18}
=\frac{6\sqrt{179}}{18}
=\frac{\sqrt{179}}{3}
$