x+(x-1.25)+1/2x=4.75

Solution for x+(x-1.25)+1/2x=4.75 equation:

x+(x-1.25)+1/2x=4.75

We move all terms to the left:

x+(x-1.25)+1/2x-(4.75)=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+(x-1.25)+1/2x-4.75=0

We get rid of parentheses

x+x+1/2x-1.25-4.75=0

We multiply all the terms by the denominator


x*2x+x*2x-(1.25)*2x-(4.75)*2x+1=0

We multiply parentheses

x*2x+x*2x-2.5x-9.5x+1=0

Wy multiply elements

2x^2+2x^2-2.5x-9.5x+1=0

We add all the numbers together, and all the variables

4x^2-12x+1=0

a = 4; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·4·1
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{2}}{2*4}=\frac{12-8\sqrt{2}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{2}}{2*4}=\frac{12+8\sqrt{2}}{8}
$