Solve D=5(2x^2-x+3)-2(x^2-2x+4)

$$D = 5 ( 2 x ^ { 2 } - x + 3 ) - 2 ( x ^ { 2 } - 2 x + 4 )$$

Solve for D

$$D=8x^{2}-x+7$$

Solution Steps

Use the distributive property to multiply 5 by 2x^{2}-x+3.

$$D=10x^{2}-5x+15-2\left(x^{2}-2x+4\right)$$

Use the distributive property to multiply -2 by x^{2}-2x+4.

$$D=10x^{2}-5x+15-2x^{2}+4x-8$$

Combine 10x^{2} and -2x^{2} to get 8x^{2}.

$$D=8x^{2}-5x+15+4x-8$$

Combine -5x and 4x to get -x.

$$D=8x^{2}-x+15-8$$

Subtract 8 from 15 to get 7.

$$D=8x^{2}-x+7$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{32D-223}+1}{16}$$

$$x=\frac{\sqrt{32D-223}+1}{16}$$

Solve for x

$$x=\frac{-\sqrt{32D-223}+1}{16}$$

$$x=\frac{\sqrt{32D-223}+1}{16}\text{, }D\geq \frac{223}{32}$$