3/2x+30=2x-30

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

3/2x+30=2x-30

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2+60x+60x+3=0

We add all the numbers together, and all the variables

-4x^2+120x+3=0

a = -4; b = 120; c = +3;
Δ = b2-4ac
Δ = 1202-4·(-4)·3
Δ = 14448
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:

$\sqrt{\Delta}=\sqrt{14448}=\sqrt{16*903}=\sqrt{16}*\sqrt{903}=4\sqrt{903}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-4\sqrt{903}}{2*-4}=\frac{-120-4\sqrt{903}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+4\sqrt{903}}{2*-4}=\frac{-120+4\sqrt{903}}{-8}
$