1/2x+30=2x

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Solution for 1/2x+30=2x equation:



1/2x+30=2x
We move all terms to the left:
1/2x+30-(2x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We add all the numbers together, and all the variables
-2x+1/2x+30=0
We multiply all the terms by the denominator
-2x*2x+30*2x+1=0
Wy multiply elements
-4x^2+60x+1=0
a = -4; b = 60; c = +1;
Δ = b2-4ac
Δ = 602-4·(-4)·1
Δ = 3616
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:
$\sqrt{\Delta}=\sqrt{3616}=\sqrt{16*226}=\sqrt{16}*\sqrt{226}=4\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{226}}{2*-4}=\frac{-60-4\sqrt{226}}{-8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{226}}{2*-4}=\frac{-60+4\sqrt{226}}{-8} $

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