1/2x+2=-x+7

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Solution for 1/2x+2=-x+7 equation:



1/2x+2=-x+7
We move all terms to the left:
1/2x+2-(-x+7)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We add all the numbers together, and all the variables
1/2x-(-1x+7)+2=0
We get rid of parentheses
1/2x+1x-7+2=0
We multiply all the terms by the denominator
1x*2x-7*2x+2*2x+1=0
Wy multiply elements
2x^2-14x+4x+1=0
We add all the numbers together, and all the variables
2x^2-10x+1=0
a = 2; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·2·1
Δ = 92
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:
$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{23}}{2*2}=\frac{10-2\sqrt{23}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{23}}{2*2}=\frac{10+2\sqrt{23}}{4} $

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