8-1/2q=4+q

Solution for 8-1/2q=4+q equation:

8-1/2q=4+q

We move all terms to the left:

8-1/2q-(4+q)=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+4)+8=0

We get rid of parentheses

-1/2q-q-4+8=0

We multiply all the terms by the denominator


-q*2q-4*2q+8*2q-1=0

Wy multiply elements

-2q^2-8q+16q-1=0

We add all the numbers together, and all the variables

-2q^2+8q-1=0

a = -2; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·(-2)·(-1)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{14}}{2*-2}=\frac{-8-2\sqrt{14}}{-4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{14}}{2*-2}=\frac{-8+2\sqrt{14}}{-4}
$