(4x+24)(3x+19)=180

Solution for (4x+24)(3x+19)=180 equation:

(4x+24)(3x+19)=180

We move all terms to the left:

(4x+24)(3x+19)-(180)=0

We multiply parentheses ..

(+12x^2+76x+72x+456)-180=0

We get rid of parentheses

12x^2+76x+72x+456-180=0

We add all the numbers together, and all the variables

12x^2+148x+276=0

a = 12; b = 148; c = +276;
Δ = b2-4ac
Δ = 1482-4·12·276
Δ = 8656
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:

$\sqrt{\Delta}=\sqrt{8656}=\sqrt{16*541}=\sqrt{16}*\sqrt{541}=4\sqrt{541}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(148)-4\sqrt{541}}{2*12}=\frac{-148-4\sqrt{541}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(148)+4\sqrt{541}}{2*12}=\frac{-148+4\sqrt{541}}{24}
$