10/2x-2(x-10)=11

Solution for 10/2x-2(x-10)=11 equation:

10/2x-2(x-10)=11

We move all terms to the left:

10/2x-2(x-10)-(11)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply parentheses

10/2x-2x+20-11=0

We multiply all the terms by the denominator


-2x*2x+20*2x-11*2x+10=0

Wy multiply elements

-4x^2+40x-22x+10=0

We add all the numbers together, and all the variables

-4x^2+18x+10=0

a = -4; b = 18; c = +10;
Δ = b2-4ac
Δ = 182-4·(-4)·10
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-22}{2*-4}=\frac{-40}{-8}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+22}{2*-4}=\frac{4}{-8}
=-1/2
$