(4x+5)(x+8)=0

Solution for (4x+5)(x+8)=0 equation:

(4x+5)(x+8)=0

We multiply parentheses ..

(+4x^2+32x+5x+40)=0

We get rid of parentheses

4x^2+32x+5x+40=0

We add all the numbers together, and all the variables

4x^2+37x+40=0

a = 4; b = 37; c = +40;
Δ = b2-4ac
Δ = 372-4·4·40
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-27}{2*4}=\frac{-64}{8}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+27}{2*4}=\frac{-10}{8}
=-1+1/4
$