x+5/2x-4=1

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

x+5/2x-4=1

We move all terms to the left:

x+5/2x-4-(1)=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+5/2x-5=0

We multiply all the terms by the denominator


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

Wy multiply elements

2x^2-10x+5=0

a = 2; b = -10; c = +5;
Δ = b2-4ac
Δ = -102-4·2·5
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{15}}{2*2}=\frac{10-2\sqrt{15}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{15}}{2*2}=\frac{10+2\sqrt{15}}{4}
$