0.75q^2-q-5=0

Solution for 0.75q^2-q-5=0 equation:

0.75q^2-q-5=0

We add all the numbers together, and all the variables

0.75q^2-1q-5=0

a = 0.75; b = -1; c = -5;
Δ = b2-4ac
Δ = -12-4·0.75·(-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{-(-1)-4}{2*0.75}=\frac{-3}{1.5}
=-2
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+4}{2*0.75}=\frac{5}{1.5}
=3+0.5/1.5
$