Find the Roots (Zeros) 17x^2-21x=-3x^2-5

$17 x^{2} - 21 x = - 3 x^{2} - 5$

Step 1

Move all terms containing $x$ to the left side of the equation.

Add $3 x^{2}$ to both sides of the equation.

$17 x^{2} - 21 x + 3 x^{2} = - 5$

Add $17 x^{2}$ and $3 x^{2}$ .

$20 x^{2} - 21 x = - 5$

Step 2

Add $5$ to both sides of the equation.

$20 x^{2} - 21 x + 5 = 0$

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 $a = 20$ , $b = - 21$ , and $c = 5$ into the quadratic formula and solve for $x$ .

$\frac{21 \pm \sqrt{{(- 21)}^{2} - 4 \cdot (20 \cdot 5)}}{2 \cdot 20}$

Step 5

Simplify.

Simplify the numerator.

Raise $- 21$ to the power of $2$ .

$x = \frac{21 \pm \sqrt{441 - 4 \cdot 20 \cdot 5}}{2 \cdot 20}$

Multiply $- 4 \cdot 20 \cdot 5$ .

Multiply $- 4$ by $20$ .

$x = \frac{21 \pm \sqrt{441 - 80 \cdot 5}}{2 \cdot 20}$

Multiply $- 80$ by $5$ .

$x = \frac{21 \pm \sqrt{441 - 400}}{2 \cdot 20}$

Subtract $400$ from $441$ .

$x = \frac{21 \pm \sqrt{41}}{2 \cdot 20}$

Multiply $2$ by $20$ .

$x = \frac{21 \pm \sqrt{41}}{40}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{21 \pm \sqrt{41}}{40}$

Decimal Form:

$x = 0.68507810 \dots, 0.36492189 \dots$

Step 7