Solve (-2x^2+5x+3)-A=4x^2+3x-7

$$( - 2 x ^ { 2 } + 5 x + 3 ) - A = 4 x ^ { 2 } + 3 x - 7$$

Solve for A

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

Steps for Solving Linear Equation

Add 2x^{2} to both sides.

$$5x+3-A=4x^{2}+3x-7+2x^{2}$$

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$5x+3-A=6x^{2}+3x-7$$

Subtract 5x from both sides.

$$3-A=6x^{2}+3x-7-5x$$

Combine 3x and -5x to get -2x.

$$3-A=6x^{2}-2x-7$$

Subtract 3 from both sides.

$$-A=6x^{2}-2x-7-3$$

Subtract 3 from -7 to get -10.

$$-A=6x^{2}-2x-10$$

Divide both sides by -1.

$$\frac{-A}{-1}=\frac{6x^{2}-2x-10}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$A=\frac{6x^{2}-2x-10}{-1}$$

Divide 6x^{2}-2x-10 by -1.

$$A=10+2x-6x^{2}$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{61-6A}+1}{6}$$

$$x=\frac{\sqrt{61-6A}+1}{6}$$

Solve for x

$$x=\frac{-\sqrt{61-6A}+1}{6}$$

$$x=\frac{\sqrt{61-6A}+1}{6}\text{, }A\leq \frac{61}{6}$$