3/2x+x=45

Solution for 3/2x+x=45 equation:

3/2x+x=45

We move all terms to the left:

3/2x+x-(45)=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+3/2x-45=0

We multiply all the terms by the denominator


x*2x-45*2x+3=0

Wy multiply elements

2x^2-90x+3=0

a = 2; b = -90; c = +3;
Δ = b2-4ac
Δ = -902-4·2·3
Δ = 8076
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8076}=\sqrt{4*2019}=\sqrt{4}*\sqrt{2019}=2\sqrt{2019}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{2019}}{2*2}=\frac{90-2\sqrt{2019}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{2019}}{2*2}=\frac{90+2\sqrt{2019}}{4}
$