Solve 3x^2-8x^2+16=0

$$3 x ^ { 2 } - 8 x ^ { 2 } + 16 = 0$$

Solve for x

$$x = \frac{4 \sqrt{5}}{5} \approx 1.788854382$$

$$x = -\frac{4 \sqrt{5}}{5} \approx -1.788854382$$

Steps by Finding Square Root

Combine 3x^{2} and -8x^{2} to get -5x^{2}.

$$-5x^{2}+16=0$$

Subtract 16 from both sides. Anything subtracted from zero gives its negation.

$$-5x^{2}=-16$$

Divide both sides by -5.

$$x^{2}=\frac{-16}{-5}$$

Fraction \frac{-16}{-5} can be simplified to \frac{16}{5} by removing the negative sign from both the numerator and the denominator.

$$x^{2}=\frac{16}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{5}}{5} x=-\frac{4\sqrt{5}}{5}$$

Steps Using the Quadratic Formula

Combine 3x^{2} and -8x^{2} to get -5x^{2}.

$$-5x^{2}+16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -5 for a, 0 for b, and 16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5\right)\times 16}}{2\left(-5\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5\right)\times 16}}{2\left(-5\right)}$$

Multiply -4 times -5.

$$x=\frac{0±\sqrt{20\times 16}}{2\left(-5\right)}$$

Multiply 20 times 16.

$$x=\frac{0±\sqrt{320}}{2\left(-5\right)}$$

Take the square root of 320.

$$x=\frac{0±8\sqrt{5}}{2\left(-5\right)}$$

Multiply 2 times -5.

$$x=\frac{0±8\sqrt{5}}{-10}$$

Now solve the equation x=\frac{0±8\sqrt{5}}{-10} when ± is plus.

$$x=-\frac{4\sqrt{5}}{5}$$

Now solve the equation x=\frac{0±8\sqrt{5}}{-10} when ± is minus.

$$x=\frac{4\sqrt{5}}{5}$$

The equation is now solved.

$$x=-\frac{4\sqrt{5}}{5} x=\frac{4\sqrt{5}}{5}$$