100-x+1/2x=90

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Solution for 100-x+1/2x=90 equation:



100-x+1/2x=90
We move all terms to the left:
100-x+1/2x-(90)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We add all the numbers together, and all the variables
-1x+1/2x+10=0
We multiply all the terms by the denominator
-1x*2x+10*2x+1=0
Wy multiply elements
-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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