48=1/2(2x)+(4x)

Solution for 48=1/2(2x)+(4x) equation:

48=1/2(2x)+(4x)

We move all terms to the left:

48-(1/2(2x)+(4x))=0


Domain of the equation: 22x+4x)!=0

x∈R


We add all the numbers together, and all the variables

-(+4x+1/22x)+48=0

We get rid of parentheses

-4x-1/22x+48=0

We multiply all the terms by the denominator


-4x*22x+48*22x-1=0

Wy multiply elements

-88x^2+1056x-1=0

a = -88; b = 1056; c = -1;
Δ = b2-4ac
Δ = 10562-4·(-88)·(-1)
Δ = 1114784
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:

$\sqrt{\Delta}=\sqrt{1114784}=\sqrt{16*69674}=\sqrt{16}*\sqrt{69674}=4\sqrt{69674}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1056)-4\sqrt{69674}}{2*-88}=\frac{-1056-4\sqrt{69674}}{-176}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1056)+4\sqrt{69674}}{2*-88}=\frac{-1056+4\sqrt{69674}}{-176}
$