1/2x+1-3x=10

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Solution for 1/2x+1-3x=10 equation:



1/2x+1-3x=10
We move all terms to the left:
1/2x+1-3x-(10)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We add all the numbers together, and all the variables
-3x+1/2x-9=0
We multiply all the terms by the denominator
-3x*2x-9*2x+1=0
Wy multiply elements
-6x^2-18x+1=0
a = -6; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·(-6)·1
Δ = 348
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:
$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{87}}{2*-6}=\frac{18-2\sqrt{87}}{-12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{87}}{2*-6}=\frac{18+2\sqrt{87}}{-12} $

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