X+(x-1.25)+1/2x=4.27

Solution for X+(x-1.25)+1/2x=4.27 equation:

X+(X-1.25)+1/2X=4.27

We move all terms to the left:

X+(X-1.25)+1/2X-(4.27)=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-4.27=0

We get rid of parentheses

X+X+1/2X-1.25-4.27=0

We multiply all the terms by the denominator


X*2X+X*2X-(1.25)*2X-(4.27)*2X+1=0

We multiply parentheses

X*2X+X*2X-2.5X-8.54X+1=0

Wy multiply elements

2X^2+2X^2-2.5X-8.54X+1=0

We add all the numbers together, and all the variables

4X^2-11.04X+1=0

a = 4; b = -11.04; c = +1;
Δ = b2-4ac
Δ = -11.042-4·4·1
Δ = 105.8816
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{-(-11.04)-\sqrt{105.8816}}{2*4}=\frac{11.04-\sqrt{105.8816}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11.04)+\sqrt{105.8816}}{2*4}=\frac{11.04+\sqrt{105.8816}}{8}
$