4^x-5/2.2^x+2+4=0

Solution for 4^x-5/2.2^x+2+4=0 equation:

4^x-5/2.2^x+2+4=0


Domain of the equation: 2.2^x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4^x-5/2.2^x+6=0

We multiply all the terms by the denominator


4^x*2.2^x+6*2.2^x-5=0

Wy multiply elements

8x^2+12x-5=0

a = 8; b = 12; c = -5;
Δ = b2-4ac
Δ = 122-4·8·(-5)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{19}}{2*8}=\frac{-12-4\sqrt{19}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{19}}{2*8}=\frac{-12+4\sqrt{19}}{16}
$