x^2/0.10-x=1.77(10)^-4

Solution for x^2/0.10-x=1.77(10)^-4 equation:

x^2/0.10-x=1.77(10)^-4

We move all terms to the left:

x^2/0.10-x-(1.77(10)^-4)=0

We add all the numbers together, and all the variables

x^2/0.10-1x-0.101654300263=0

We multiply all the terms by the denominator


x^2-1x*0.10-(0.101654300263)*0.10=0

We add all the numbers together, and all the variables

x^2-1x*0.10-0.0101654300263=0

Wy multiply elements

x^2-0.1x-0.0101654300263=0

a = 1; b = -0.1; c = -0.0101654300263;
Δ = b2-4ac
Δ = -0.12-4·1·(-0.0101654300263)
Δ = 0.0506617201052
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{-(-0.1)-\sqrt{0.0506617201052}}{2*1}=\frac{0.1-\sqrt{0.0506617201052}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.1)+\sqrt{0.0506617201052}}{2*1}=\frac{0.1+\sqrt{0.0506617201052}}{2}
$