32000+10x/100=45000+7x/10x

Solution for 32000+10x/100=45000+7x/10x equation:

32000+10x/100=45000+7x/10x

We move all terms to the left:

32000+10x/100-(45000+7x/10x)=0


Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

10x/100-(7x/10x+45000)+32000=0

We get rid of parentheses

10x/100-7x/10x-45000+32000=0

We calculate fractions


100x^2/1000x+(-700x)/1000x-45000+32000=0

We add all the numbers together, and all the variables

100x^2/1000x+(-700x)/1000x-13000=0

We multiply all the terms by the denominator


100x^2+(-700x)-13000*1000x=0

Wy multiply elements

100x^2+(-700x)-13000000x=0

We get rid of parentheses

100x^2-700x-13000000x=0

We add all the numbers together, and all the variables

100x^2-13000700x=0

a = 100; b = -13000700; c = 0;
Δ = b2-4ac
Δ = -130007002-4·100·0
Δ = 169018200490000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169018200490000}=13000700$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13000700)-13000700}{2*100}=\frac{0}{200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13000700)+13000700}{2*100}=\frac{26001400}{200}
=130007
$