5q(q-3)+2(7.5q+6)=32

Solution for 5q(q-3)+2(7.5q+6)=32 equation:

5q(q-3)+2(7.5q+6)=32

We move all terms to the left:

5q(q-3)+2(7.5q+6)-(32)=0

We multiply parentheses

5q^2-15q+14q+12-32=0

We add all the numbers together, and all the variables

5q^2-1q-20=0

a = 5; b = -1; c = -20;
Δ = b2-4ac
Δ = -12-4·5·(-20)
Δ = 401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{401}}{2*5}=\frac{1-\sqrt{401}}{10}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{401}}{2*5}=\frac{1+\sqrt{401}}{10}
$