Solve C=x(3x+5)-8(3-x)

$$C = x ( 3 x + 5 ) - 8 ( 3 - x )$$

Solve for C

$$C=3x^{2}+13x-24$$

Solution Steps

Use the distributive property to multiply x by 3x+5.

$$C=3x^{2}+5x-8\left(3-x\right)$$

Use the distributive property to multiply -8 by 3-x.

$$C=3x^{2}+5x-24+8x$$

Combine 5x and 8x to get 13x.

$$C=3x^{2}+13x-24$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{12C+457}-13}{6}$$

$$x=\frac{\sqrt{12C+457}-13}{6}$$

Solve for x

$$x=\frac{-\sqrt{12C+457}-13}{6}$$

$$x=\frac{\sqrt{12C+457}-13}{6}\text{, }C\geq -\frac{457}{12}$$