(4x-10)4x=80

Solution for (4x-10)4x=80 equation:

(4x-10)4x=80

We move all terms to the left:

(4x-10)4x-(80)=0

We multiply parentheses

16x^2-40x-80=0

a = 16; b = -40; c = -80;
Δ = b2-4ac
Δ = -402-4·16·(-80)
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{-(-40)-8\sqrt{105}}{2*16}=\frac{40-8\sqrt{105}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{105}}{2*16}=\frac{40+8\sqrt{105}}{32}
$