2/3q+5=2q+13

Solution for 2/3q+5=2q+13 equation:

2/3q+5=2q+13

We move all terms to the left:

2/3q+5-(2q+13)=0


Domain of the equation: 3q!=0

q!=0/3

q!=0

q∈R


We get rid of parentheses

2/3q-2q-13+5=0

We multiply all the terms by the denominator


-2q*3q-13*3q+5*3q+2=0

Wy multiply elements

-6q^2-39q+15q+2=0

We add all the numbers together, and all the variables

-6q^2-24q+2=0

a = -6; b = -24; c = +2;
Δ = b2-4ac
Δ = -242-4·(-6)·2
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{39}}{2*-6}=\frac{24-4\sqrt{39}}{-12}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{39}}{2*-6}=\frac{24+4\sqrt{39}}{-12}
$