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

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}
$