Solve 3x^2+5/7=19

$$\frac { 3 x ^ { 2 } + 5 } { 7 } = 19$$

Solve for x

$$x = \frac{8 \sqrt{6}}{3} \approx 6.531972647$$

$$x = -\frac{8 \sqrt{6}}{3} \approx -6.531972647$$

Steps by Finding Square Root

Multiply both sides by 7.

$$3x^{2}+5=19\times 7$$

Multiply 19 and 7 to get 133.

$$3x^{2}+5=133$$

Subtract 5 from both sides.

$$3x^{2}=133-5$$

Subtract 5 from 133 to get 128.

$$3x^{2}=128$$

Divide both sides by 3.

$$x^{2}=\frac{128}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{8\sqrt{6}}{3} x=-\frac{8\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Multiply both sides by 7.

$$3x^{2}+5=19\times 7$$

Multiply 19 and 7 to get 133.

$$3x^{2}+5=133$$

Subtract 133 from both sides.

$$3x^{2}+5-133=0$$

Subtract 133 from 5 to get -128.

$$3x^{2}-128=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -128 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-128\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-128\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-128\right)}}{2\times 3}$$

Multiply -12 times -128.

$$x=\frac{0±\sqrt{1536}}{2\times 3}$$

Take the square root of 1536.

$$x=\frac{0±16\sqrt{6}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±16\sqrt{6}}{6}$$

Now solve the equation x=\frac{0±16\sqrt{6}}{6} when ± is plus.

$$x=\frac{8\sqrt{6}}{3}$$

Now solve the equation x=\frac{0±16\sqrt{6}}{6} when ± is minus.

$$x=-\frac{8\sqrt{6}}{3}$$

The equation is now solved.

$$x=\frac{8\sqrt{6}}{3} x=-\frac{8\sqrt{6}}{3}$$