Find the Roots (Zeros) -21x+10=-10x^2

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

Add $10 x^{2}$ to both sides of the equation.

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

Use the quadratic formula to find the solutions.

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

Substitute the values $a = 10$ , $b = - 21$ , and $c = 10$ into the quadratic formula and solve for $x$ .

$\frac{21 \pm \sqrt{{(- 21)}^{2} - 4 \cdot (10 \cdot 10)}}{2 \cdot 10}$

Simplify.

Simplify the numerator.

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

$x = \frac{21 \pm \sqrt{441 - 4 \cdot 10 \cdot 10}}{2 \cdot 10}$

Multiply $- 4$ by $10$ .

$x = \frac{21 \pm \sqrt{441 - 40 \cdot 10}}{2 \cdot 10}$

Multiply $- 40$ by $10$ .

$x = \frac{21 \pm \sqrt{441 - 400}}{2 \cdot 10}$

Subtract $400$ from $441$ .

$x = \frac{21 \pm \sqrt{41}}{2 \cdot 10}$

Multiply $2$ by $10$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 1.37015621 \dots, 0.72984378 \dots$