x+3/2*x=150

Solution for x+3/2*x=150 equation:

x+3/2x=150

We move all terms to the left:

x+3/2x-(150)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-150*2x+3=0

Wy multiply elements

2x^2-300x+3=0

a = 2; b = -300; c = +3;
Δ = b2-4ac
Δ = -3002-4·2·3
Δ = 89976
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:

$\sqrt{\Delta}=\sqrt{89976}=\sqrt{4*22494}=\sqrt{4}*\sqrt{22494}=2\sqrt{22494}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-2\sqrt{22494}}{2*2}=\frac{300-2\sqrt{22494}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+2\sqrt{22494}}{2*2}=\frac{300+2\sqrt{22494}}{4}
$