(x^2)/20-(3/5)x+1=0

Solution for (x^2)/20-(3/5)x+1=0 equation:

(x^2)/20-(3/5)x+1=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x^2/20-(+3/5)x+1=0

We multiply parentheses

x^2/20-3x^2+1=0

We multiply all the terms by the denominator


x^2-3x^2*20+1*20=0

We add all the numbers together, and all the variables

x^2-3x^2*20+20=0

Wy multiply elements

x^2-60x^2+20=0

We add all the numbers together, and all the variables

-59x^2+20=0

a = -59; b = 0; c = +20;
Δ = b2-4ac
Δ = 02-4·(-59)·20
Δ = 4720
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:

$\sqrt{\Delta}=\sqrt{4720}=\sqrt{16*295}=\sqrt{16}*\sqrt{295}=4\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{295}}{2*-59}=\frac{0-4\sqrt{295}}{-118}
=-\frac{4\sqrt{295}}{-118}
=-\frac{2\sqrt{295}}{-59}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{295}}{2*-59}=\frac{0+4\sqrt{295}}{-118}
=\frac{4\sqrt{295}}{-118}
=\frac{2\sqrt{295}}{-59}
$