1/2q+q=3000-1000

Solution for 1/2q+q=3000-1000 equation:

1/2q+q=3000-1000

We move all terms to the left:

1/2q+q-(3000-1000)=0


Domain of the equation: 2q!=0

q!=0/2

q!=0

q∈R


We add all the numbers together, and all the variables

1/2q+q-2000=0

We add all the numbers together, and all the variables

q+1/2q-2000=0

We multiply all the terms by the denominator


q*2q-2000*2q+1=0

Wy multiply elements

2q^2-4000q+1=0

a = 2; b = -4000; c = +1;
Δ = b2-4ac
Δ = -40002-4·2·1
Δ = 15999992
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{15999992}=\sqrt{4*3999998}=\sqrt{4}*\sqrt{3999998}=2\sqrt{3999998}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4000)-2\sqrt{3999998}}{2*2}=\frac{4000-2\sqrt{3999998}}{4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4000)+2\sqrt{3999998}}{2*2}=\frac{4000+2\sqrt{3999998}}{4}
$