1/2x+5=x+15

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Solution for 1/2x+5=x+15 equation:



1/2x+5=x+15
We move all terms to the left:
1/2x+5-(x+15)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We get rid of parentheses
1/2x-x-15+5=0
We multiply all the terms by the denominator
-x*2x-15*2x+5*2x+1=0
Wy multiply elements
-2x^2-30x+10x+1=0
We add all the numbers together, and all the variables
-2x^2-20x+1=0
a = -2; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·(-2)·1
Δ = 408
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:
$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{102}}{2*-2}=\frac{20-2\sqrt{102}}{-4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{102}}{2*-2}=\frac{20+2\sqrt{102}}{-4} $

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