2/3q=423q=4

Solution for 2/3q=423q=4 equation:

2/3q=423q=4

We move all terms to the left:

2/3q-(423q)=0


Domain of the equation: 3q!=0

q!=0/3

q!=0

q∈R


We add all the numbers together, and all the variables

-423q+2/3q=0

We multiply all the terms by the denominator


-423q*3q+2=0

Wy multiply elements

-1269q^2+2=0

a = -1269; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-1269)·2
Δ = 10152
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:

$\sqrt{\Delta}=\sqrt{10152}=\sqrt{36*282}=\sqrt{36}*\sqrt{282}=6\sqrt{282}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{282}}{2*-1269}=\frac{0-6\sqrt{282}}{-2538}
=-\frac{6\sqrt{282}}{-2538}
=-\frac{\sqrt{282}}{-423}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{282}}{2*-1269}=\frac{0+6\sqrt{282}}{-2538}
=\frac{6\sqrt{282}}{-2538}
=\frac{\sqrt{282}}{-423}
$