0=9q^2-15q+4

Solution for 0=9q^2-15q+4 equation:

0=9q^2-15q+4

We move all terms to the left:

0-(9q^2-15q+4)=0

We add all the numbers together, and all the variables

-(9q^2-15q+4)=0

We get rid of parentheses

-9q^2+15q-4=0

a = -9; b = 15; c = -4;
Δ = b2-4ac
Δ = 152-4·(-9)·(-4)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-9}{2*-9}=\frac{-24}{-18}
=1+1/3
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+9}{2*-9}=\frac{-6}{-18}
=1/3
$