3/2x-x=30

Solution for 3/2x-x=30 equation:

3/2x-x=30

We move all terms to the left:

3/2x-x-(30)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/2x-30=0

We multiply all the terms by the denominator


-1x*2x-30*2x+3=0

Wy multiply elements

-2x^2-60x+3=0

a = -2; b = -60; c = +3;
Δ = b2-4ac
Δ = -602-4·(-2)·3
Δ = 3624
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:

$\sqrt{\Delta}=\sqrt{3624}=\sqrt{4*906}=\sqrt{4}*\sqrt{906}=2\sqrt{906}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{906}}{2*-2}=\frac{60-2\sqrt{906}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{906}}{2*-2}=\frac{60+2\sqrt{906}}{-4}
$