(1/2)x+3=13

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Solution for (1/2)x+3=13 equation:



(1/2)x+3=13
We move all terms to the left:
(1/2)x+3-(13)=0
Domain of the equation: 2)x!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+1/2)x+3-13=0
We add all the numbers together, and all the variables
(+1/2)x-10=0
We multiply parentheses
x^2-10=0
a = 1; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·1·(-10)
Δ = 40
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:
$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{10}}{2*1}=\frac{0-2\sqrt{10}}{2} =-\frac{2\sqrt{10}}{2} =-\sqrt{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{10}}{2*1}=\frac{0+2\sqrt{10}}{2} =\frac{2\sqrt{10}}{2} =\sqrt{10} $

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