8-(2/3q)=q

Solution for 8-(2/3q)=q equation:

8-(2/3q)=q

We move all terms to the left:

8-(2/3q)-(q)=0


Domain of the equation: 3q)!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

-(+2/3q)-q+8=0

We add all the numbers together, and all the variables

-1q-(+2/3q)+8=0

We get rid of parentheses

-1q-2/3q+8=0

We multiply all the terms by the denominator


-1q*3q+8*3q-2=0

Wy multiply elements

-3q^2+24q-2=0

a = -3; b = 24; c = -2;
Δ = b2-4ac
Δ = 242-4·(-3)·(-2)
Δ = 552
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:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{138}}{2*-3}=\frac{-24-2\sqrt{138}}{-6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{138}}{2*-3}=\frac{-24+2\sqrt{138}}{-6}
$