2x=(-1/9)x^2

Solution for 2x=(-1/9)x^2 equation:

2x=(-1/9)x^2

We move all terms to the left:

2x-((-1/9)x^2)=0


Domain of the equation: 9)x^2)!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


2x*9)x^2)-((-1=0

Wy multiply elements

18x^2-1=0

a = 18; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·18·(-1)
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*18}=\frac{0-6\sqrt{2}}{36}
=-\frac{6\sqrt{2}}{36}
=-\frac{\sqrt{2}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*18}=\frac{0+6\sqrt{2}}{36}
=\frac{6\sqrt{2}}{36}
=\frac{\sqrt{2}}{6}
$