(7q-46)(3q+6)=180

Solution for (7q-46)(3q+6)=180 equation:

(7q-46)(3q+6)=180

We move all terms to the left:

(7q-46)(3q+6)-(180)=0

We multiply parentheses ..

(+21q^2+42q-138q-276)-180=0

We get rid of parentheses

21q^2+42q-138q-276-180=0

We add all the numbers together, and all the variables

21q^2-96q-456=0

a = 21; b = -96; c = -456;
Δ = b2-4ac
Δ = -962-4·21·(-456)
Δ = 47520
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:

$\sqrt{\Delta}=\sqrt{47520}=\sqrt{144*330}=\sqrt{144}*\sqrt{330}=12\sqrt{330}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-12\sqrt{330}}{2*21}=\frac{96-12\sqrt{330}}{42}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+12\sqrt{330}}{2*21}=\frac{96+12\sqrt{330}}{42}
$