2x+970-100x=633/2x

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Solution for 2x+970-100x=633/2x equation:



2x+970-100x=633/2x
We move all terms to the left:
2x+970-100x-(633/2x)=0
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
2x-100x-(+633/2x)+970=0
We add all the numbers together, and all the variables
-98x-(+633/2x)+970=0
We get rid of parentheses
-98x-633/2x+970=0
We multiply all the terms by the denominator
-98x*2x+970*2x-633=0
Wy multiply elements
-196x^2+1940x-633=0
a = -196; b = 1940; c = -633;
Δ = b2-4ac
Δ = 19402-4·(-196)·(-633)
Δ = 3267328
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:
$\sqrt{\Delta}=\sqrt{3267328}=\sqrt{256*12763}=\sqrt{256}*\sqrt{12763}=16\sqrt{12763}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1940)-16\sqrt{12763}}{2*-196}=\frac{-1940-16\sqrt{12763}}{-392} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1940)+16\sqrt{12763}}{2*-196}=\frac{-1940+16\sqrt{12763}}{-392} $

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