(3x+16)(9x+4)=180

Solution for (3x+16)(9x+4)=180 equation:

(3x+16)(9x+4)=180

We move all terms to the left:

(3x+16)(9x+4)-(180)=0

We multiply parentheses ..

(+27x^2+12x+144x+64)-180=0

We get rid of parentheses

27x^2+12x+144x+64-180=0

We add all the numbers together, and all the variables

27x^2+156x-116=0

a = 27; b = 156; c = -116;
Δ = b2-4ac
Δ = 1562-4·27·(-116)
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-192}{2*27}=\frac{-348}{54}
=-6+4/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+192}{2*27}=\frac{36}{54}
=2/3
$