x-7/2x=5+20

Solution for x-7/2x=5+20 equation:

x-7/2x=5+20

We move all terms to the left:

x-7/2x-(5+20)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x-7/2x-25=0

We multiply all the terms by the denominator


x*2x-25*2x-7=0

Wy multiply elements

2x^2-50x-7=0

a = 2; b = -50; c = -7;
Δ = b2-4ac
Δ = -502-4·2·(-7)
Δ = 2556
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:

$\sqrt{\Delta}=\sqrt{2556}=\sqrt{36*71}=\sqrt{36}*\sqrt{71}=6\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-6\sqrt{71}}{2*2}=\frac{50-6\sqrt{71}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+6\sqrt{71}}{2*2}=\frac{50+6\sqrt{71}}{4}
$