(5x+24)(x+3)=0

Solution for (5x+24)(x+3)=0 equation:

(5x+24)(x+3)=0

We multiply parentheses ..

(+5x^2+15x+24x+72)=0

We get rid of parentheses

5x^2+15x+24x+72=0

We add all the numbers together, and all the variables

5x^2+39x+72=0

a = 5; b = 39; c = +72;
Δ = b2-4ac
Δ = 392-4·5·72
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-9}{2*5}=\frac{-48}{10}
=-4+4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+9}{2*5}=\frac{-30}{10}
=-3
$