10x+1/10x+20=0,75

Solution for 10x+1/10x+20=0,75 equation:

10x+1/10x+20=0.75

We move all terms to the left:

10x+1/10x+20-(0.75)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

10x+1/10x+19.25=0

We multiply all the terms by the denominator


10x*10x+(19.25)*10x+1=0

We multiply parentheses

10x*10x+192.5x+1=0

Wy multiply elements

100x^2+192.5x+1=0

a = 100; b = 192.5; c = +1;
Δ = b2-4ac
Δ = 192.52-4·100·1
Δ = 36656.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192.5)-\sqrt{36656.25}}{2*100}=\frac{-192.5-\sqrt{36656.25}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192.5)+\sqrt{36656.25}}{2*100}=\frac{-192.5+\sqrt{36656.25}}{200}
$