5x(8x+20)=40

Solution for 5x(8x+20)=40 equation:

5x(8x+20)=40

We move all terms to the left:

5x(8x+20)-(40)=0

We multiply parentheses

40x^2+100x-40=0

a = 40; b = 100; c = -40;
Δ = b2-4ac
Δ = 1002-4·40·(-40)
Δ = 16400
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:

$\sqrt{\Delta}=\sqrt{16400}=\sqrt{400*41}=\sqrt{400}*\sqrt{41}=20\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{41}}{2*40}=\frac{-100-20\sqrt{41}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{41}}{2*40}=\frac{-100+20\sqrt{41}}{80}
$