Solve the Quadratic Equation: x²+3x-4=2x²

Given the equation:

$x^2 + 3x - 4 = 2x^2$

Step 1: Move all terms to one side:

Subtract $2x^2$ from both sides to get:

$x^2 + 3x - 4 - 2x^2 = 0$

Simplify this to:

$-x^2 + 3x - 4 = 0$

Step 2: Rearrange to standard form:

Multiply the entire equation by -1 for simplicity:

$x^2 - 3x + 4 = 0$

Step 3: Solve the quadratic equation using the quadratic formula:

Here, $a = 1$, $b = -3$, $c = 4$.

Plug into the quadratic formula:

$x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4 \times 1 \times 4}}{2 \times 1}$

$x = \frac{3 \pm \sqrt{9 - 16}}{2}$

$x = \frac{3 \pm \sqrt{-7}}{2}$

Step 4: Interpret the result:

The discriminant ($b^2 - 4ac$) is negative, $-7$, indicating no real solutions.

Conclusion: The equation has no solution in the set of real numbers.

In comparison with the provided choices, the correct choice is:

No solution