(2780-10x)-100/x-40=100

Solution for (2780-10x)-100/x-40=100 equation:

(2780-10x)-100/x-40=100

We move all terms to the left:

(2780-10x)-100/x-40-(100)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

(-10x+2780)-100/x-40-100=0

We add all the numbers together, and all the variables

(-10x+2780)-100/x-140=0

We get rid of parentheses

-10x-100/x+2780-140=0

We multiply all the terms by the denominator


-10x*x+2780*x-140*x-100=0

We add all the numbers together, and all the variables

2640x-10x*x-100=0

Wy multiply elements

-10x^2+2640x-100=0

a = -10; b = 2640; c = -100;
Δ = b2-4ac
Δ = 26402-4·(-10)·(-100)
Δ = 6965600
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:

$\sqrt{\Delta}=\sqrt{6965600}=\sqrt{400*17414}=\sqrt{400}*\sqrt{17414}=20\sqrt{17414}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2640)-20\sqrt{17414}}{2*-10}=\frac{-2640-20\sqrt{17414}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2640)+20\sqrt{17414}}{2*-10}=\frac{-2640+20\sqrt{17414}}{-20}
$