X+(x-1.25)+1/2x=3.5

Solution for X+(x-1.25)+1/2x=3.5 equation:

X+(X-1.25)+1/2X=3.5

We move all terms to the left:

X+(X-1.25)+1/2X-(3.5)=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+(X-1.25)+1/2X-3.5=0

We get rid of parentheses

X+X+1/2X-1.25-3.5=0

We multiply all the terms by the denominator


X*2X+X*2X-(1.25)*2X-(3.5)*2X+1=0

We multiply parentheses

X*2X+X*2X-2.5X-7X+1=0

Wy multiply elements

2X^2+2X^2-2.5X-7X+1=0

We add all the numbers together, and all the variables

4X^2-9.5X+1=0

a = 4; b = -9.5; c = +1;
Δ = b2-4ac
Δ = -9.52-4·4·1
Δ = 74.25
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{-(-9.5)-\sqrt{74.25}}{2*4}=\frac{9.5-\sqrt{74.25}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9.5)+\sqrt{74.25}}{2*4}=\frac{9.5+\sqrt{74.25}}{8}
$