2x(4x+9)+(3x-12)=180

Solution for 2x(4x+9)+(3x-12)=180 equation:

2x(4x+9)+(3x-12)=180

We move all terms to the left:

2x(4x+9)+(3x-12)-(180)=0

We multiply parentheses

8x^2+18x+(3x-12)-180=0

We get rid of parentheses

8x^2+18x+3x-12-180=0

We add all the numbers together, and all the variables

8x^2+21x-192=0

a = 8; b = 21; c = -192;
Δ = b2-4ac
Δ = 212-4·8·(-192)
Δ = 6585
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-\sqrt{6585}}{2*8}=\frac{-21-\sqrt{6585}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{6585}}{2*8}=\frac{-21+\sqrt{6585}}{16}
$