1/2q+q=180

Solution for 1/2q+q=180 equation:

1/2q+q=180

We move all terms to the left:

1/2q+q-(180)=0


Domain of the equation: 2q!=0

q!=0/2

q!=0

q∈R


We add all the numbers together, and all the variables

q+1/2q-180=0

We multiply all the terms by the denominator


q*2q-180*2q+1=0

Wy multiply elements

2q^2-360q+1=0

a = 2; b = -360; c = +1;
Δ = b2-4ac
Δ = -3602-4·2·1
Δ = 129592
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:

$\sqrt{\Delta}=\sqrt{129592}=\sqrt{4*32398}=\sqrt{4}*\sqrt{32398}=2\sqrt{32398}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-2\sqrt{32398}}{2*2}=\frac{360-2\sqrt{32398}}{4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+2\sqrt{32398}}{2*2}=\frac{360+2\sqrt{32398}}{4}
$