21/2x-7=8+x

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Solution for 21/2x-7=8+x equation:



21/2x-7=8+x
We move all terms to the left:
21/2x-7-(8+x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We add all the numbers together, and all the variables
21/2x-(x+8)-7=0
We get rid of parentheses
21/2x-x-8-7=0
We multiply all the terms by the denominator
-x*2x-8*2x-7*2x+21=0
Wy multiply elements
-2x^2-16x-14x+21=0
We add all the numbers together, and all the variables
-2x^2-30x+21=0
a = -2; b = -30; c = +21;
Δ = b2-4ac
Δ = -302-4·(-2)·21
Δ = 1068
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:
$\sqrt{\Delta}=\sqrt{1068}=\sqrt{4*267}=\sqrt{4}*\sqrt{267}=2\sqrt{267}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{267}}{2*-2}=\frac{30-2\sqrt{267}}{-4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{267}}{2*-2}=\frac{30+2\sqrt{267}}{-4} $

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