(x+16)(4x-5)=180

Solution for (x+16)(4x-5)=180 equation:

(x+16)(4x-5)=180

We move all terms to the left:

(x+16)(4x-5)-(180)=0

We multiply parentheses ..

(+4x^2-5x+64x-80)-180=0

We get rid of parentheses

4x^2-5x+64x-80-180=0

We add all the numbers together, and all the variables

4x^2+59x-260=0

a = 4; b = 59; c = -260;
Δ = b2-4ac
Δ = 592-4·4·(-260)
Δ = 7641
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:

$\sqrt{\Delta}=\sqrt{7641}=\sqrt{9*849}=\sqrt{9}*\sqrt{849}=3\sqrt{849}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-3\sqrt{849}}{2*4}=\frac{-59-3\sqrt{849}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+3\sqrt{849}}{2*4}=\frac{-59+3\sqrt{849}}{8}
$