6q-q^2-5=0

Solution for 6q-q^2-5=0 equation:

6q-q^2-5=0

We add all the numbers together, and all the variables

-1q^2+6q-5=0

a = -1; b = 6; c = -5;
Δ = b2-4ac
Δ = 62-4·(-1)·(-5)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4}{2*-1}=\frac{-10}{-2}
=+5
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4}{2*-1}=\frac{-2}{-2}
=1
$