4x(8x-7)=16

Solution for 4x(8x-7)=16 equation:

4x(8x-7)=16

We move all terms to the left:

4x(8x-7)-(16)=0

We multiply parentheses

32x^2-28x-16=0

a = 32; b = -28; c = -16;
Δ = b2-4ac
Δ = -282-4·32·(-16)
Δ = 2832
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:

$\sqrt{\Delta}=\sqrt{2832}=\sqrt{16*177}=\sqrt{16}*\sqrt{177}=4\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{177}}{2*32}=\frac{28-4\sqrt{177}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{177}}{2*32}=\frac{28+4\sqrt{177}}{64}
$