2x=3/2x+30

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

2x=3/2x+30

We move all terms to the left:

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


Domain of the equation: 2x+30)!=0

x∈R


We get rid of parentheses

2x-3/2x-30=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-60x-3=0

a = 4; b = -60; c = -3;
Δ = b2-4ac
Δ = -602-4·4·(-3)
Δ = 3648
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:

$\sqrt{\Delta}=\sqrt{3648}=\sqrt{64*57}=\sqrt{64}*\sqrt{57}=8\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-8\sqrt{57}}{2*4}=\frac{60-8\sqrt{57}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+8\sqrt{57}}{2*4}=\frac{60+8\sqrt{57}}{8}
$