x+x+3/2x=75

Solution for x+x+3/2x=75 equation:

x+x+3/2x=75

We move all terms to the left:

x+x+3/2x-(75)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+3/2x-75=0

We multiply all the terms by the denominator


2x*2x-75*2x+3=0

Wy multiply elements

4x^2-150x+3=0

a = 4; b = -150; c = +3;
Δ = b2-4ac
Δ = -1502-4·4·3
Δ = 22452
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:

$\sqrt{\Delta}=\sqrt{22452}=\sqrt{4*5613}=\sqrt{4}*\sqrt{5613}=2\sqrt{5613}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5613}}{2*4}=\frac{150-2\sqrt{5613}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5613}}{2*4}=\frac{150+2\sqrt{5613}}{8}
$