5x+6-2x+4+x-7+1/2x=200

Solution for 5x+6-2x+4+x-7+1/2x=200 equation:

5x+6-2x+4+x-7+1/2x=200

We move all terms to the left:

5x+6-2x+4+x-7+1/2x-(200)=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-197=0

We multiply all the terms by the denominator


4x*2x-197*2x+1=0

Wy multiply elements

8x^2-394x+1=0

a = 8; b = -394; c = +1;
Δ = b2-4ac
Δ = -3942-4·8·1
Δ = 155204
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:

$\sqrt{\Delta}=\sqrt{155204}=\sqrt{4*38801}=\sqrt{4}*\sqrt{38801}=2\sqrt{38801}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-394)-2\sqrt{38801}}{2*8}=\frac{394-2\sqrt{38801}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-394)+2\sqrt{38801}}{2*8}=\frac{394+2\sqrt{38801}}{16}
$