(3x+16)(5x-54)=180

Solution for (3x+16)(5x-54)=180 equation:

(3x+16)(5x-54)=180

We move all terms to the left:

(3x+16)(5x-54)-(180)=0

We multiply parentheses ..

(+15x^2-162x+80x-864)-180=0

We get rid of parentheses

15x^2-162x+80x-864-180=0

We add all the numbers together, and all the variables

15x^2-82x-1044=0

a = 15; b = -82; c = -1044;
Δ = b2-4ac
Δ = -822-4·15·(-1044)
Δ = 69364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{69364}=\sqrt{4*17341}=\sqrt{4}*\sqrt{17341}=2\sqrt{17341}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{17341}}{2*15}=\frac{82-2\sqrt{17341}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{17341}}{2*15}=\frac{82+2\sqrt{17341}}{30}
$