Solve for x
x=\frac{3-3x_{1}^{2}}{2}
Solve for x_1 (complex solution)
x_{1}=-\frac{\sqrt{9-6x}}{3}
x_{1}=\frac{\sqrt{9-6x}}{3}
Solve for x_1
x_{1}=\frac{\sqrt{9-6x}}{3}
x_{1}=-\frac{\sqrt{9-6x}}{3}\text{, }x\leq \frac{3}{2}
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2x-3=-3x_{1}^{2}
Subtract 3x_{1}^{2} from both sides. Anything subtracted from zero gives its negation.
2x=-3x_{1}^{2}+3
Add 3 to both sides.
2x=3-3x_{1}^{2}
The equation is in standard form.
\frac{2x}{2}=\frac{3-3x_{1}^{2}}{2}
Divide both sides by 2.
x=\frac{3-3x_{1}^{2}}{2}
Dividing by 2 undoes the multiplication by 2.
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