13q^2+9q-144=0

Solution for 13q^2+9q-144=0 equation:

13q^2+9q-144=0

a = 13; b = 9; c = -144;
Δ = b2-4ac
Δ = 92-4·13·(-144)
Δ = 7569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7569}=87$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-87}{2*13}=\frac{-96}{26}
=-3+9/13
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+87}{2*13}=\frac{78}{26}
=3
$