4(2x-5)2x=100

Solution for 4(2x-5)2x=100 equation:

4(2x-5)2x=100

We move all terms to the left:

4(2x-5)2x-(100)=0

We multiply parentheses

16x^2-40x-100=0

a = 16; b = -40; c = -100;
Δ = b2-4ac
Δ = -402-4·16·(-100)
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40\sqrt{5}}{2*16}=\frac{40-40\sqrt{5}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40\sqrt{5}}{2*16}=\frac{40+40\sqrt{5}}{32}
$