Solve 13x+2y-6=273*3x^2+473t

$$13 x + 2 y - 6 = 273 \cdot 3 x ^ { 2 } + 473 t$$

Solve for t

$$t=\frac{-819x^{2}+13x+2y-6}{473}$$

Steps for Solving Linear Equation

Multiply 273 and 3 to get 819.

$$13x+2y-6=819x^{2}+473t$$

Swap sides so that all variable terms are on the left hand side.

$$819x^{2}+473t=13x+2y-6$$

Subtract 819x^{2} from both sides.

$$473t=13x+2y-6-819x^{2}$$

The equation is in standard form.

$$473t=-819x^{2}+13x+2y-6$$

Divide both sides by 473.

$$\frac{473t}{473}=\frac{-819x^{2}+13x+2y-6}{473}$$

Dividing by 473 undoes the multiplication by 473.

$$t=\frac{-819x^{2}+13x+2y-6}{473}$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{6552y-1549548t-19487}}{1638}+\frac{1}{126}$$

$$x=\frac{\sqrt{6552y-1549548t-19487}}{1638}+\frac{1}{126}$$

Solve for x

$$x=-\frac{\sqrt{6552y-1549548t-19487}}{1638}+\frac{1}{126}$$

$$x=\frac{\sqrt{6552y-1549548t-19487}}{1638}+\frac{1}{126}\text{, }y\geq \frac{473t}{2}+\frac{1499}{504}$$