9*q*q-2q=8*q*q-8q+27

Solution for 9*q*q-2q=8*q*q-8q+27 equation:

9q*q-2q=8q*q-8q+27

We move all terms to the left:

9q*q-2q-(8q*q-8q+27)=0

We add all the numbers together, and all the variables

9q*q-2q-(-8q+8q*q+27)=0

We add all the numbers together, and all the variables

-2q+9q*q-(-8q+8q*q+27)=0

Wy multiply elements

9q^2-2q-(-8q+8q*q+27)=0

We get rid of parentheses

9q^2-2q+8q-8q*q-27=0

We add all the numbers together, and all the variables

9q^2+6q-8q*q-27=0

Wy multiply elements

9q^2-8q^2+6q-27=0

We add all the numbers together, and all the variables

q^2+6q-27=0

a = 1; b = 6; c = -27;
Δ = b2-4ac
Δ = 62-4·1·(-27)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*1}=\frac{-18}{2}
=-9
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*1}=\frac{6}{2}
=3
$