1/4q+1/5q=1

Solution for 1/4q+1/5q=1 equation:

1/4q+1/5q=1

We move all terms to the left:

1/4q+1/5q-(1)=0


Domain of the equation: 4q!=0

q!=0/4

q!=0

q∈R



Domain of the equation: 5q!=0

q!=0/5

q!=0

q∈R


We calculate fractions


5q/20q^2+4q/20q^2-1=0

We multiply all the terms by the denominator


5q+4q-1*20q^2=0

We add all the numbers together, and all the variables

9q-1*20q^2=0

Wy multiply elements

-20q^2+9q=0

a = -20; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-20)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-20}=\frac{-18}{-40}
=9/20
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-20}=\frac{0}{-40}
=0
$