1/2x+4x=34

Solution for 1/2x+4x=34 equation:

1/2x+4x=34

We move all terms to the left:

1/2x+4x-(34)=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-34=0

We multiply all the terms by the denominator


4x*2x-34*2x+1=0

Wy multiply elements

8x^2-68x+1=0

a = 8; b = -68; c = +1;
Δ = b2-4ac
Δ = -682-4·8·1
Δ = 4592
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:

$\sqrt{\Delta}=\sqrt{4592}=\sqrt{16*287}=\sqrt{16}*\sqrt{287}=4\sqrt{287}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-68)-4\sqrt{287}}{2*8}=\frac{68-4\sqrt{287}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-68)+4\sqrt{287}}{2*8}=\frac{68+4\sqrt{287}}{16}
$