8X(x+5)=40

Solution for 8X(x+5)=40 equation:

8X(X+5)=40

We move all terms to the left:

8X(X+5)-(40)=0

We multiply parentheses

8X^2+40X-40=0

a = 8; b = 40; c = -40;
Δ = b2-4ac
Δ = 402-4·8·(-40)
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-24\sqrt{5}}{2*8}=\frac{-40-24\sqrt{5}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+24\sqrt{5}}{2*8}=\frac{-40+24\sqrt{5}}{16}
$