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 = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{35}}{2*2}=\frac{10-2\sqrt{35}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{35}}{2*2}=\frac{10+2\sqrt{35}}{4}
$