1/2x+15=2x-50

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Solution for 1/2x+15=2x-50 equation:



1/2x+15=2x-50
We move all terms to the left:
1/2x+15-(2x-50)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We get rid of parentheses
1/2x-2x+50+15=0
We multiply all the terms by the denominator
-2x*2x+50*2x+15*2x+1=0
Wy multiply elements
-4x^2+100x+30x+1=0
We add all the numbers together, and all the variables
-4x^2+130x+1=0
a = -4; b = 130; c = +1;
Δ = b2-4ac
Δ = 1302-4·(-4)·1
Δ = 16916
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:
$\sqrt{\Delta}=\sqrt{16916}=\sqrt{4*4229}=\sqrt{4}*\sqrt{4229}=2\sqrt{4229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-2\sqrt{4229}}{2*-4}=\frac{-130-2\sqrt{4229}}{-8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+2\sqrt{4229}}{2*-4}=\frac{-130+2\sqrt{4229}}{-8} $

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