1/5q=9-2.5q

Solution for 1/5q=9-2.5q equation:

1/5q=9-2.5q

We move all terms to the left:

1/5q-(9-2.5q)=0


Domain of the equation: 5q!=0

q!=0/5

q!=0

q∈R


We add all the numbers together, and all the variables

1/5q-(-2.5q+9)=0

We get rid of parentheses

1/5q+2.5q-9=0

We multiply all the terms by the denominator


(2.5q)*5q-9*5q+1=0

We add all the numbers together, and all the variables

(+2.5q)*5q-9*5q+1=0

We multiply parentheses

10q^2-9*5q+1=0

Wy multiply elements

10q^2-45q+1=0

a = 10; b = -45; c = +1;
Δ = b2-4ac
Δ = -452-4·10·1
Δ = 1985
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{1985}}{2*10}=\frac{45-\sqrt{1985}}{20}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1985}}{2*10}=\frac{45+\sqrt{1985}}{20}
$