7/2x=2x+0.5

Solution for 7/2x=2x+0.5 equation:

7/2x=2x+0.5

We move all terms to the left:

7/2x-(2x+0.5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

7/2x-2x-0.5=0

We multiply all the terms by the denominator


-2x*2x-(0.5)*2x+7=0

We multiply parentheses

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

Wy multiply elements

-4x^2-x+7=0

We add all the numbers together, and all the variables

-4x^2-1x+7=0

a = -4; b = -1; c = +7;
Δ = b2-4ac
Δ = -12-4·(-4)·7
Δ = 113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{113}}{2*-4}=\frac{1-\sqrt{113}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{113}}{2*-4}=\frac{1+\sqrt{113}}{-8}
$