2x+18=3x+1/2x+1.5

Solution for 2x+18=3x+1/2x+1.5 equation:

2x+18=3x+1/2x+1.5

We move all terms to the left:

2x+18-(3x+1/2x+1.5)=0


Domain of the equation: 2x+1.5)!=0

x∈R


We get rid of parentheses

2x-3x-1/2x-1.5+18=0

We multiply all the terms by the denominator


2x*2x-3x*2x-(1.5)*2x+18*2x-1=0

We multiply parentheses

2x*2x-3x*2x-3x+18*2x-1=0

Wy multiply elements

4x^2-6x^2-3x+36x-1=0

We add all the numbers together, and all the variables

-2x^2+33x-1=0

a = -2; b = 33; c = -1;
Δ = b2-4ac
Δ = 332-4·(-2)·(-1)
Δ = 1081
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{-(33)-\sqrt{1081}}{2*-2}=\frac{-33-\sqrt{1081}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1081}}{2*-2}=\frac{-33+\sqrt{1081}}{-4}
$