7-x=1+1/2x

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



7-x=1+1/2x
We move all terms to the left:
7-x-(1+1/2x)=0
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
-x-(1/2x+1)+7=0
We add all the numbers together, and all the variables
-1x-(1/2x+1)+7=0
We get rid of parentheses
-1x-1/2x-1+7=0
We multiply all the terms by the denominator
-1x*2x-1*2x+7*2x-1=0
Wy multiply elements
-2x^2-2x+14x-1=0
We add all the numbers together, and all the variables
-2x^2+12x-1=0
a = -2; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·(-2)·(-1)
Δ = 136
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:
$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{34}}{2*-2}=\frac{-12-2\sqrt{34}}{-4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{34}}{2*-2}=\frac{-12+2\sqrt{34}}{-4} $

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