Solve for x y=3x^2+7x+m

$y = 3 x^{2} + 7 x + m$

Step 1

Rewrite the equation as $3 x^{2} + 7 x + m = y$ .

$3 x^{2} + 7 x + m = y$

Step 2

Subtract $y$ from both sides of the equation.

$3 x^{2} + 7 x + m - y = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = 3$ , $b = 7$ , and $c = m - y$ into the quadratic formula and solve for $x$ .

$\frac{- 7 \pm \sqrt{7^{2} - 4 \cdot (3 \cdot (m - y))}}{2 \cdot 3}$

Step 5

Simplify.

Simplify the numerator.

Raise $7$ to the power of $2$ .

$x = \frac{- 7 \pm \sqrt{49 - 4 \cdot 3 \cdot (m - y)}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$x = \frac{- 7 \pm \sqrt{49 - 12 \cdot (m - y)}}{2 \cdot 3}$

Apply the distributive property.

$x = \frac{- 7 \pm \sqrt{49 - 12 m - 12 (- y)}}{2 \cdot 3}$

Multiply $- 1$ by $- 12$ .

$x = \frac{- 7 \pm \sqrt{49 - 12 m + 12 y}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 7 \pm \sqrt{49 - 12 m + 12 y}}{6}$

Step 6

The final answer is the combination of both solutions.

$x = - \frac{7 - \sqrt{49 - 12 m + 12 y}}{6}$

$x = - \frac{7 + \sqrt{- 12 m + 12 y + 49}}{6}$