-2x+5/2x=17

Solution for -2x+5/2x=17 equation:

-2x+5/2x=17

We move all terms to the left:

-2x+5/2x-(17)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


-2x*2x-17*2x+5=0

Wy multiply elements

-4x^2-34x+5=0

a = -4; b = -34; c = +5;
Δ = b2-4ac
Δ = -342-4·(-4)·5
Δ = 1236
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:

$\sqrt{\Delta}=\sqrt{1236}=\sqrt{4*309}=\sqrt{4}*\sqrt{309}=2\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{309}}{2*-4}=\frac{34-2\sqrt{309}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{309}}{2*-4}=\frac{34+2\sqrt{309}}{-8}
$