z x ^ { 2 } - 6,5 x - 3,5 = 0
Solve for z
z=\frac{13x+7}{2x^{2}}
x\neq 0
Solve for x
\left\{\begin{matrix}\\x=-\frac{7}{13}\approx -0,538461538\text{, }&\text{unconditionally}\\x=\frac{\sqrt{14z+42,25}+6,5}{2z}\text{; }x=\frac{-\sqrt{14z+42,25}+6,5}{2z}\text{, }&z\neq 0\text{ and }z\geq -\frac{169}{56}\end{matrix}\right.
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zx^{2}-3,5=6,5x
Add 6,5x to both sides. Anything plus zero gives itself.
zx^{2}=6,5x+3,5
Add 3,5 to both sides.
x^{2}z=\frac{13x+7}{2}
The equation is in standard form.
\frac{x^{2}z}{x^{2}}=\frac{13x+7}{2x^{2}}
Divide both sides by x^{2}.
z=\frac{13x+7}{2x^{2}}
Dividing by x^{2} undoes the multiplication by x^{2}.
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