28+q=1/2q

Solution for 28+q=1/2q equation:

28+q=1/2q

We move all terms to the left:

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


Domain of the equation: 2q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

q-(+1/2q)+28=0

We get rid of parentheses

q-1/2q+28=0

We multiply all the terms by the denominator


q*2q+28*2q-1=0

Wy multiply elements

2q^2+56q-1=0

a = 2; b = 56; c = -1;
Δ = b2-4ac
Δ = 562-4·2·(-1)
Δ = 3144
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:

$\sqrt{\Delta}=\sqrt{3144}=\sqrt{4*786}=\sqrt{4}*\sqrt{786}=2\sqrt{786}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{786}}{2*2}=\frac{-56-2\sqrt{786}}{4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{786}}{2*2}=\frac{-56+2\sqrt{786}}{4}
$