Solve Using the Quadratic Formula 5x^2-3x+10=2x^2

$5 x^{2} - 3 x + 10 = 2 x^{2}$

Move all terms to the left side of the equation and simplify.

Subtract $2 x^{2}$ from both sides of the equation.

$5 x^{2} - 3 x + 10 - 2 x^{2} = 0$

Subtract $2 x^{2}$ from $5 x^{2}$ .

$3 x^{2} - 3 x + 10 = 0$

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 3$ , $b = - 3$ , and $c = 10$ into the quadratic formula and solve for $x$ .

$\frac{3 \pm \sqrt{{(- 3)}^{2} - 4 \cdot (3 \cdot 10)}}{2 \cdot 3}$

Simplify.

Simplify the numerator.

Raise $- 3$ to the power of $2$ .

$x = \frac{3 \pm \sqrt{9 - 4 \cdot 3 \cdot 10}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$x = \frac{3 \pm \sqrt{9 - 12 \cdot 10}}{2 \cdot 3}$

Multiply $- 12$ by $10$ .

$x = \frac{3 \pm \sqrt{9 - 120}}{2 \cdot 3}$

Subtract $120$ from $9$ .

$x = \frac{3 \pm \sqrt{- 111}}{2 \cdot 3}$

Rewrite $- 111$ as $- 1 (111)$ .

$x = \frac{3 \pm \sqrt{- 1 \cdot 111}}{2 \cdot 3}$

Rewrite $\sqrt{- 1 (111)}$ as $\sqrt{- 1} \cdot \sqrt{111}$ .

$x = \frac{3 \pm \sqrt{- 1} \cdot \sqrt{111}}{2 \cdot 3}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{3 \pm i \sqrt{111}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{3 \pm i \sqrt{111}}{6}$