Solve y=1/2(x+3)(x-4)

$$y = \frac { 1 } { 2 } ( x + 3 ) ( x - 4 )$$

Solve for y

$$y=\frac{\left(x-4\right)\left(x+3\right)}{2}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by x+3.

$$y=\left(\frac{1}{2}x+\frac{3}{2}\right)\left(x-4\right)$$

Use the distributive property to multiply \frac{1}{2}x+\frac{3}{2} by x-4 and combine like terms.

$$y=\frac{1}{2}x^{2}-\frac{1}{2}x-6$$

Solve for x (complex solution)

$$x=\frac{\sqrt{8y+49}+1}{2}$$

$$x=\frac{-\sqrt{8y+49}+1}{2}$$

Solve for x

$$x=\frac{\sqrt{8y+49}+1}{2}$$

$$x=\frac{-\sqrt{8y+49}+1}{2}\text{, }y\geq -\frac{49}{8}$$