100-1/2q=2q+10

Solution for 100-1/2q=2q+10 equation:

100-1/2q=2q+10

We move all terms to the left:

100-1/2q-(2q+10)=0


Domain of the equation: 2q!=0

q!=0/2

q!=0

q∈R


We get rid of parentheses

-1/2q-2q-10+100=0

We multiply all the terms by the denominator


-2q*2q-10*2q+100*2q-1=0

Wy multiply elements

-4q^2-20q+200q-1=0

We add all the numbers together, and all the variables

-4q^2+180q-1=0

a = -4; b = 180; c = -1;
Δ = b2-4ac
Δ = 1802-4·(-4)·(-1)
Δ = 32384
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:

$\sqrt{\Delta}=\sqrt{32384}=\sqrt{64*506}=\sqrt{64}*\sqrt{506}=8\sqrt{506}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-8\sqrt{506}}{2*-4}=\frac{-180-8\sqrt{506}}{-8}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+8\sqrt{506}}{2*-4}=\frac{-180+8\sqrt{506}}{-8}
$