2240-x=12/100.x

Solution for 2240-x=12/100.x equation:

2240-x=12/100.x

We move all terms to the left:

2240-x-(12/100.x)=0


Domain of the equation: 100.x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(+12/100.x)+2240=0

We add all the numbers together, and all the variables

-1x-(+12/100.x)+2240=0

We get rid of parentheses

-1x-12/100.x+2240=0

We multiply all the terms by the denominator


-1x*100.x+2240*100.x-12=0

Wy multiply elements

-100x^2+224000x-12=0

a = -100; b = 224000; c = -12;
Δ = b2-4ac
Δ = 2240002-4·(-100)·(-12)
Δ = 50175995200
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:

$\sqrt{\Delta}=\sqrt{50175995200}=\sqrt{1600*31359997}=\sqrt{1600}*\sqrt{31359997}=40\sqrt{31359997}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(224000)-40\sqrt{31359997}}{2*-100}=\frac{-224000-40\sqrt{31359997}}{-200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(224000)+40\sqrt{31359997}}{2*-100}=\frac{-224000+40\sqrt{31359997}}{-200}
$