150,000=3/2x+x

Solution for 150,000=3/2x+x equation:

150.000=3/2x+x

We move all terms to the left:

150.000-(3/2x+x)=0


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

x∈R


We add all the numbers together, and all the variables

-(+x+3/2x)+150.000=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-x-3/2x+150=0

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}
$