8x(5x+4)=5

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

8x(5x+4)=5

We move all terms to the left:

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

We multiply parentheses

40x^2+32x-5=0

a = 40; b = 32; c = -5;
Δ = b2-4ac
Δ = 322-4·40·(-5)
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{114}}{2*40}=\frac{-32-4\sqrt{114}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{114}}{2*40}=\frac{-32+4\sqrt{114}}{80}
$