X+1/2x=7.5

Solution for X+1/2x=7.5 equation:

X+1/2X=7.5

We move all terms to the left:

X+1/2X-(7.5)=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-7.5=0

We multiply all the terms by the denominator


X*2X-(7.5)*2X+1=0

We multiply parentheses

X*2X-15X+1=0

Wy multiply elements

2X^2-15X+1=0

a = 2; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·2·1
Δ = 217
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{-(-15)-\sqrt{217}}{2*2}=\frac{15-\sqrt{217}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{217}}{2*2}=\frac{15+\sqrt{217}}{4}
$