5/3q+q=24

Solution for 5/3q+q=24 equation:

5/3q+q=24

We move all terms to the left:

5/3q+q-(24)=0


Domain of the equation: 3q!=0

q!=0/3

q!=0

q∈R


We add all the numbers together, and all the variables

q+5/3q-24=0

We multiply all the terms by the denominator


q*3q-24*3q+5=0

Wy multiply elements

3q^2-72q+5=0

a = 3; b = -72; c = +5;
Δ = b2-4ac
Δ = -722-4·3·5
Δ = 5124
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:

$\sqrt{\Delta}=\sqrt{5124}=\sqrt{4*1281}=\sqrt{4}*\sqrt{1281}=2\sqrt{1281}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1281}}{2*3}=\frac{72-2\sqrt{1281}}{6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1281}}{2*3}=\frac{72+2\sqrt{1281}}{6}
$