16x(x+5)=5

Solution for 16x(x+5)=5 equation:

16x(x+5)=5

We move all terms to the left:

16x(x+5)-(5)=0

We multiply parentheses

16x^2+80x-5=0

a = 16; b = 80; c = -5;
Δ = b2-4ac
Δ = 802-4·16·(-5)
Δ = 6720
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:

$\sqrt{\Delta}=\sqrt{6720}=\sqrt{64*105}=\sqrt{64}*\sqrt{105}=8\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-8\sqrt{105}}{2*16}=\frac{-80-8\sqrt{105}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+8\sqrt{105}}{2*16}=\frac{-80+8\sqrt{105}}{32}
$