x(.5x^2+9.27*10^-6)=1.1567*10^-7

Solution for x(.5x^2+9.27*10^-6)=1.1567*10^-7 equation:

x(.5x^2+9.27*10^-6)=1.1567*10^-7

We move all terms to the left:

x(.5x^2+9.27*10^-6)-(1.1567*10^-7)=0

We add all the numbers together, and all the variables

x(.5x^2+9.27*10^-6)-7-1.1567E=0

We multiply parentheses

x^2+92.7x^2-6x-7-1.1567E=0

We add all the numbers together, and all the variables

93.7x^2-6x-10.144236590979=0

a = 93.7; b = -6; c = -10.144236590979;
Δ = b2-4ac
Δ = -62-4·93.7·(-10.144236590979)
Δ = 3838.0598742989
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{-(-6)-\sqrt{3838.0598742989}}{2*93.7}=\frac{6-\sqrt{3838.0598742989}}{187.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+\sqrt{3838.0598742989}}{2*93.7}=\frac{6+\sqrt{3838.0598742989}}{187.4}
$