(2/5)q-3=9

Solution for (2/5)q-3=9 equation:

(2/5)q-3=9

We move all terms to the left:

(2/5)q-3-(9)=0


Domain of the equation: 5)q!=0

q!=0/1

q!=0

q∈R


We add all the numbers together, and all the variables

(+2/5)q-3-9=0

We add all the numbers together, and all the variables

(+2/5)q-12=0

We multiply parentheses

2q^2-12=0

a = 2; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·2·(-12)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*2}=\frac{0-4\sqrt{6}}{4}
=-\frac{4\sqrt{6}}{4}
=-\sqrt{6}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*2}=\frac{0+4\sqrt{6}}{4}
=\frac{4\sqrt{6}}{4}
=\sqrt{6}
$