x-1/2x-1.25=5

Solution for x-1/2x-1.25=5 equation:

x-1/2x-1.25=5

We move all terms to the left:

x-1/2x-1.25-(5)=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-1/2x-6.25=0

We multiply all the terms by the denominator


x*2x-(6.25)*2x-1=0

We multiply parentheses

x*2x-12.5x-1=0

Wy multiply elements

2x^2-12.5x-1=0

a = 2; b = -12.5; c = -1;
Δ = b2-4ac
Δ = -12.52-4·2·(-1)
Δ = 164.25
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{-(-12.5)-\sqrt{164.25}}{2*2}=\frac{12.5-\sqrt{164.25}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12.5)+\sqrt{164.25}}{2*2}=\frac{12.5+\sqrt{164.25}}{4}
$