4/5+1/2+3/x=41/20,x=

Solution for 4/5+1/2+3/x=41/20,x= equation:

4/5+1/2+3/x=41/20.x=

We move all terms to the left:

4/5+1/2+3/x-(41/20.x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 20.x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/x-(+41/20.x)+4/5+1/2=0

We get rid of parentheses

3/x-41/20.x+4/5+1/2=0

We calculate fractions


320x^2/200x^2+200x^2/200x^2+600x/200x^2+(-2050x)/200x^2=0

Fractions to decimals

320x^2/200x^2+600x/200x^2+(-2050x)/200x^2+1=0

We multiply all the terms by the denominator


320x^2+600x+(-2050x)+1*200x^2=0

Wy multiply elements

320x^2+200x^2+600x+(-2050x)=0

We get rid of parentheses

320x^2+200x^2+600x-2050x=0

We add all the numbers together, and all the variables

520x^2-1450x=0

a = 520; b = -1450; c = 0;
Δ = b2-4ac
Δ = -14502-4·520·0
Δ = 2102500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2102500}=1450$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1450)-1450}{2*520}=\frac{0}{1040}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1450)+1450}{2*520}=\frac{2900}{1040}
=2+41/52
$