3/2x=2x+30

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



3/2x=2x+30
We move all terms to the left:
3/2x-(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=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} $

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