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Solve for a (complex solution)
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Solve for b (complex solution)
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Solve for a
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Solve for b
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ax^{2}+c=3x-bx
Subtract bx from both sides.
ax^{2}=3x-bx-c
Subtract c from both sides.
x^{2}a=-bx+3x-c
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{-bx+3x-c}{x^{2}}
Divide both sides by x^{2}.
a=\frac{-bx+3x-c}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
bx+c=3x-ax^{2}
Subtract ax^{2} from both sides.
bx=3x-ax^{2}-c
Subtract c from both sides.
bx=-ax^{2}+3x-c
Reorder the terms.
xb=-ax^{2}+3x-c
The equation is in standard form.
\frac{xb}{x}=\frac{-ax^{2}+3x-c}{x}
Divide both sides by x.
b=\frac{-ax^{2}+3x-c}{x}
Dividing by x undoes the multiplication by x.
b=-ax-\frac{c}{x}+3
Divide -ax^{2}+3x-c by x.
ax^{2}+c=3x-bx
Subtract bx from both sides.
ax^{2}=3x-bx-c
Subtract c from both sides.
x^{2}a=-bx+3x-c
The equation is in standard form.
\frac{x^{2}a}{x^{2}}=\frac{-bx+3x-c}{x^{2}}
Divide both sides by x^{2}.
a=\frac{-bx+3x-c}{x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
bx+c=3x-ax^{2}
Subtract ax^{2} from both sides.
bx=3x-ax^{2}-c
Subtract c from both sides.
bx=-ax^{2}+3x-c
Reorder the terms.
xb=-ax^{2}+3x-c
The equation is in standard form.
\frac{xb}{x}=\frac{-ax^{2}+3x-c}{x}
Divide both sides by x.
b=\frac{-ax^{2}+3x-c}{x}
Dividing by x undoes the multiplication by x.
b=-ax-\frac{c}{x}+3
Divide -ax^{2}+3x-c by x.