2(1/2x-5)2x=44

Solution for 2(1/2x-5)2x=44 equation:

2(1/2x-5)2x=44

We move all terms to the left:

2(1/2x-5)2x-(44)=0


Domain of the equation: 2x-5)2x!=0

x∈R


We multiply parentheses

4x^2-20x-44=0

a = 4; b = -20; c = -44;
Δ = b2-4ac
Δ = -202-4·4·(-44)
Δ = 1104
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:

$\sqrt{\Delta}=\sqrt{1104}=\sqrt{16*69}=\sqrt{16}*\sqrt{69}=4\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{69}}{2*4}=\frac{20-4\sqrt{69}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{69}}{2*4}=\frac{20+4\sqrt{69}}{8}
$