1x+1.5=4+1/2x

Solution for 1x+1.5=4+1/2x equation:

1x+1.5=4+1/2x

We move all terms to the left:

1x+1.5-(4+1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1x-(1/2x+4)+1.5=0

We add all the numbers together, and all the variables

x-(1/2x+4)+1.5=0

We get rid of parentheses

x-1/2x-4+1.5=0

We multiply all the terms by the denominator


x*2x-4*2x+(1.5)*2x-1=0

We multiply parentheses

x*2x-4*2x+3x-1=0

Wy multiply elements

2x^2-8x+3x-1=0

We add all the numbers together, and all the variables

2x^2-5x-1=0

a = 2; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·2·(-1)
Δ = 33
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{-(-5)-\sqrt{33}}{2*2}=\frac{5-\sqrt{33}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{33}}{2*2}=\frac{5+\sqrt{33}}{4}
$