7/2x+1/2x=2x=10/2=9/2x

Solution for 7/2x+1/2x=2x=10/2=9/2x equation:

7/2x+1/2x=2x=10/2=9/2x

We move all terms to the left:

7/2x+1/2x-(2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+7/2x+1/2x=0

We multiply all the terms by the denominator


-2x*2x+7+1=0

We add all the numbers together, and all the variables

-2x*2x+8=0

Wy multiply elements

-4x^2+8=0

a = -4; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-4)·8
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{2}}{2*-4}=\frac{0-8\sqrt{2}}{-8}
=-\frac{8\sqrt{2}}{-8}
=-\frac{\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{2}}{2*-4}=\frac{0+8\sqrt{2}}{-8}
=\frac{8\sqrt{2}}{-8}
=\frac{\sqrt{2}}{-1}
$