x^2/0.10=4.0*10^-9

Solution for x^2/0.10=4.0*10^-9 equation:

x^2/0.10=4.0*10^-9

We move all terms to the left:

x^2/0.10-(4.0*10^-9)=0

We add all the numbers together, and all the variables

x^2/0.10-9-4.0E=0

We multiply all the terms by the denominator


x^2-9*0.10-(4.0E)*0.10=0

We add all the numbers together, and all the variables

x^2-9*0.10-(10.873127313836)*0.10=0

We add all the numbers together, and all the variables

x^2-1.9873127313836=0

a = 1; b = 0; c = -1.9873127313836;
Δ = b2-4ac
Δ = 02-4·1·(-1.9873127313836)
Δ = 7.9492509255344
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)-\sqrt{7.9492509255344}}{2*1}=\frac{0-\sqrt{7.9492509255344}}{2}
=-\frac{\sqrt{}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{7.9492509255344}}{2*1}=\frac{0+\sqrt{7.9492509255344}}{2}
=\frac{\sqrt{}}{2}
$