q-1.9+1/q=2-1.9q

Solution for q-1.9+1/q=2-1.9q equation:

q-1.9+1/q=2-1.9q

We move all terms to the left:

q-1.9+1/q-(2-1.9q)=0


Domain of the equation: q!=0

q∈R


We add all the numbers together, and all the variables

q+1/q-(-1.9q+2)-1.9=0

We get rid of parentheses

q+1/q+1.9q-2-1.9=0

We multiply all the terms by the denominator


q*q+(1.9q)*q-2*q-(1.9)*q+1=0

We add all the numbers together, and all the variables

q*q+(+1.9q)*q-2*q-(1.9)*q+1=0

We add all the numbers together, and all the variables

-2q+q*q+(+1.9q)*q-(1.9)*q+1=0

We multiply parentheses

q^2-2q+q*q-1.9q+1=0

Wy multiply elements

q^2+q^2-2q-1.9q+1=0

We add all the numbers together, and all the variables

2q^2-3.9q+1=0

a = 2; b = -3.9; c = +1;
Δ = b2-4ac
Δ = -3.92-4·2·1
Δ = 7.21
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{-(-3.9)-\sqrt{7.21}}{2*2}=\frac{3.9-\sqrt{7.21}}{4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3.9)+\sqrt{7.21}}{2*2}=\frac{3.9+\sqrt{7.21}}{4}
$