(x+24)(4x+1)=180

Solution for (x+24)(4x+1)=180 equation:

(x+24)(4x+1)=180

We move all terms to the left:

(x+24)(4x+1)-(180)=0

We multiply parentheses ..

(+4x^2+x+96x+24)-180=0

We get rid of parentheses

4x^2+x+96x+24-180=0

We add all the numbers together, and all the variables

4x^2+97x-156=0

a = 4; b = 97; c = -156;
Δ = b2-4ac
Δ = 972-4·4·(-156)
Δ = 11905
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{-(97)-\sqrt{11905}}{2*4}=\frac{-97-\sqrt{11905}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(97)+\sqrt{11905}}{2*4}=\frac{-97+\sqrt{11905}}{8}
$