1/22x=10x-9.5

Solution for 1/22x=10x-9.5 equation:

1/22x=10x-9.5

We move all terms to the left:

1/22x-(10x-9.5)=0


Domain of the equation: 22x!=0

x!=0/22

x!=0

x∈R


We get rid of parentheses

1/22x-10x+9.5=0

We multiply all the terms by the denominator


-10x*22x+(9.5)*22x+1=0

We multiply parentheses

-10x*22x+209x+1=0

Wy multiply elements

-220x^2+209x+1=0

a = -220; b = 209; c = +1;
Δ = b2-4ac
Δ = 2092-4·(-220)·1
Δ = 44561
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{-(209)-\sqrt{44561}}{2*-220}=\frac{-209-\sqrt{44561}}{-440}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(209)+\sqrt{44561}}{2*-220}=\frac{-209+\sqrt{44561}}{-440}
$