Solve Using the Quadratic Formula 5x^2-3x+10=2x^2+21

$5 x^{2} - 3 x + 10 = 2 x^{2} + 21$

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

Move all the expressions to the left side of the equation.

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

$5 x^{2} - 3 x + 10 - 2 x^{2} = 21$

Subtract $21$ from both sides of the equation.

$5 x^{2} - 3 x + 10 - 2 x^{2} - 21 = 0$

Simplify $5 x^{2} - 3 x + 10 - 2 x^{2} - 21$ .

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

$3 x^{2} - 3 x + 10 - 21 = 0$

Subtract $21$ from $10$ .

$3 x^{2} - 3 x - 11 = 0$

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 $c = - 11$ into the quadratic formula and solve for $x$ .

$\frac{3 \pm \sqrt{{(- 3)}^{2} - 4 \cdot (3 \cdot - 11)}}{2 \cdot 3}$

Simplify.

Simplify the numerator.

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

$x = \frac{3 \pm \sqrt{9 - 4 \cdot 3 \cdot - 11}}{2 \cdot 3}$

Multiply $- 4$ by $3$ .

$x = \frac{3 \pm \sqrt{9 - 12 \cdot - 11}}{2 \cdot 3}$

Multiply $- 12$ by $- 11$ .

$x = \frac{3 \pm \sqrt{9 + 132}}{2 \cdot 3}$

Add $9$ and $132$ .

$x = \frac{3 \pm \sqrt{141}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{3 \pm \sqrt{141}}{6}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3 \pm \sqrt{141}}{6}$

Decimal Form:

$x = 2.47905701 \dots, - 1.47905701 \dots$