5.0*10^-13=x^2+0.031x

Solution for 5.0*10^-13=x^2+0.031x equation:

5.0*10^-13=x^2+0.031x

We move all terms to the left:

5.0*10^-13-(x^2+0.031x)=0

We add all the numbers together, and all the variables

-(x^2+0.031x)=0

We get rid of parentheses

-x^2-0.031x=0

We add all the numbers together, and all the variables

-1x^2-0.031x=0

a = -1; b = -0.031; c = 0;
Δ = b2-4ac
Δ = -0.0312-4·(-1)·0
Δ = 0.000961
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{-(-0.031)-\sqrt{0.000961}}{2*-1}=\frac{0.031-\sqrt{0.000961}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.031)+\sqrt{0.000961}}{2*-1}=\frac{0.031+\sqrt{0.000961}}{-2}
$