Solve 5x^2-3x=2-k

$$5 x ^ { 2 } - 3 x = 2 - k$$

Solve for k

$$k=\left(1-x\right)\left(5x+2\right)$$

Steps for Solving Linear Equation

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

$$2-k=5x^{2}-3x$$

Subtract 2 from both sides.

$$-k=5x^{2}-3x-2$$

Divide both sides by -1.

$$\frac{-k}{-1}=\frac{\left(x-1\right)\left(5x+2\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$k=\frac{\left(x-1\right)\left(5x+2\right)}{-1}$$

Divide \left(-1+x\right)\left(2+5x\right) by -1.

$$k=-\left(x-1\right)\left(5x+2\right)$$

Solve for x (complex solution)

$$x=\frac{\sqrt{49-20k}+3}{10}$$

$$x=\frac{-\sqrt{49-20k}+3}{10}$$

Solve for x

$$x=\frac{\sqrt{49-20k}+3}{10}$$

$$x=\frac{-\sqrt{49-20k}+3}{10}\text{, }k\leq \frac{49}{20}$$