x^2/110-(21/110)(x)+1=0

Solution for x^2/110-(21/110)(x)+1=0 equation:

x^2/110-(21/110)(x)+1=0


Domain of the equation: 110)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x^2/110-(+21/110)x+1=0

We multiply parentheses

x^2/110-21x^2+1=0

We multiply all the terms by the denominator


x^2-21x^2*110+1*110=0

We add all the numbers together, and all the variables

x^2-21x^2*110+110=0

Wy multiply elements

x^2-2310x^2+110=0

We add all the numbers together, and all the variables

-2309x^2+110=0

a = -2309; b = 0; c = +110;
Δ = b2-4ac
Δ = 02-4·(-2309)·110
Δ = 1015960
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:

$\sqrt{\Delta}=\sqrt{1015960}=\sqrt{4*253990}=\sqrt{4}*\sqrt{253990}=2\sqrt{253990}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{253990}}{2*-2309}=\frac{0-2\sqrt{253990}}{-4618}
=-\frac{2\sqrt{253990}}{-4618}
=-\frac{\sqrt{253990}}{-2309}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{253990}}{2*-2309}=\frac{0+2\sqrt{253990}}{-4618}
=\frac{2\sqrt{253990}}{-4618}
=\frac{\sqrt{253990}}{-2309}
$