-q^2-6q^2+144q-545=0

Solution for -q^2-6q^2+144q-545=0 equation:

-q^2-6q^2+144q-545=0

We add all the numbers together, and all the variables

-7q^2+144q-545=0

a = -7; b = 144; c = -545;
Δ = b2-4ac
Δ = 1442-4·(-7)·(-545)
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-74}{2*-7}=\frac{-218}{-14}
=15+4/7
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+74}{2*-7}=\frac{-70}{-14}
=+5
$