1/2x+4*x=56

Solution for 1/2x+4*x=56 equation:

1/2x+4x=56

We move all terms to the left:

1/2x+4x-(56)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4x+1/2x-56=0

We multiply all the terms by the denominator


4x*2x-56*2x+1=0

Wy multiply elements

8x^2-112x+1=0

a = 8; b = -112; c = +1;
Δ = b2-4ac
Δ = -1122-4·8·1
Δ = 12512
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:

$\sqrt{\Delta}=\sqrt{12512}=\sqrt{16*782}=\sqrt{16}*\sqrt{782}=4\sqrt{782}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-4\sqrt{782}}{2*8}=\frac{112-4\sqrt{782}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+4\sqrt{782}}{2*8}=\frac{112+4\sqrt{782}}{16}
$