Solve 0.5x^2-3x-y+2.5=0

$$0.5 { x }^{ 2 } -3x-y+2.5=0$$

Solve for y

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

Steps for Solving Linear Equation

Subtract 0.5x^{2} from both sides. Anything subtracted from zero gives its negation.

$$-3x-y+2.5=-0.5x^{2}$$

Add 3x to both sides.

$$-y+2.5=-0.5x^{2}+3x$$

Subtract 2.5 from both sides.

$$-y=-0.5x^{2}+3x-2.5$$

The equation is in standard form.

$$-y=-\frac{x^{2}}{2}+3x-2.5$$

Divide both sides by -1.

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

Dividing by -1 undoes the multiplication by -1.

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

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

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

Solve for x (complex solution)

$$x=\sqrt{2\left(y+2\right)}+3$$

$$x=-\sqrt{2\left(y+2\right)}+3$$

Solve for x

$$x=\sqrt{2\left(y+2\right)}+3$$

$$x=-\sqrt{2\left(y+2\right)}+3\text{, }y\geq -2$$