X+3/2x=45

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

X+3/2X=45

We move all terms to the left:

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


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


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}
$