.100-10x=1.41x(.0100+10x)

Solution for .100-10x=1.41x(.0100+10x) equation:

.100-10x=1.41x(.0100+10x)

We move all terms to the left:

.100-10x-(1.41x(.0100+10x))=0

We add all the numbers together, and all the variables

-10x-(1.41x(10x+0.01))+.100=0

We add all the numbers together, and all the variables

-10x-(1.41x(10x+0.01))+0.1=0


We calculate terms in parentheses: -(1.41x(10x+0.01)), so:

1.41x(10x+0.01)

We multiply parentheses

10x^2+0.01x

Back to the equation:

-(10x^2+0.01x)


We get rid of parentheses

-10x^2-10x-0.01x+0.1=0

We add all the numbers together, and all the variables

-10x^2-10.01x+0.1=0

a = -10; b = -10.01; c = +0.1;
Δ = b2-4ac
Δ = -10.012-4·(-10)·0.1
Δ = 104.2001
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{-(-10.01)-\sqrt{104.2001}}{2*-10}=\frac{10.01-\sqrt{104.2001}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10.01)+\sqrt{104.2001}}{2*-10}=\frac{10.01+\sqrt{104.2001}}{-20}
$