(X+8)(4x+1)=0

Solution for (X+8)(4x+1)=0 equation:

(X+8)(4X+1)=0

We multiply parentheses ..

(+4X^2+X+32X+8)=0

We get rid of parentheses

4X^2+X+32X+8=0

We add all the numbers together, and all the variables

4X^2+33X+8=0

a = 4; b = 33; c = +8;
Δ = b2-4ac
Δ = 332-4·4·8
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-31}{2*4}=\frac{-64}{8}
=-8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+31}{2*4}=\frac{-2}{8}
=-1/4
$