Solve 3x^2-38-98/4=015

$$\frac { 3 x ^ { 2 } - 38 - 98 } { 4 } = 015$$

Solve for x

$$x = \frac{2 \sqrt{102}}{3} \approx 6.733003292$$

$$x = -\frac{2 \sqrt{102}}{3} \approx -6.733003292$$

Steps by Finding Square Root

Multiply both sides of the equation by 4.

$$3x^{2}-38-98=0\times 15$$

Subtract 98 from -38 to get -136.

$$3x^{2}-136=0\times 15$$

Multiply 0 and 15 to get 0.

$$3x^{2}-136=0$$

Add 136 to both sides. Anything plus zero gives itself.

$$3x^{2}=136$$

Divide both sides by 3.

$$x^{2}=\frac{136}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{102}}{3} x=-\frac{2\sqrt{102}}{3}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4.

$$3x^{2}-38-98=0\times 15$$

Subtract 98 from -38 to get -136.

$$3x^{2}-136=0\times 15$$

Multiply 0 and 15 to get 0.

$$3x^{2}-136=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -136 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-136\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-136\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-136\right)}}{2\times 3}$$

Multiply -12 times -136.

$$x=\frac{0±\sqrt{1632}}{2\times 3}$$

Take the square root of 1632.

$$x=\frac{0±4\sqrt{102}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±4\sqrt{102}}{6}$$

Now solve the equation x=\frac{0±4\sqrt{102}}{6} when ± is plus.

$$x=\frac{2\sqrt{102}}{3}$$

Now solve the equation x=\frac{0±4\sqrt{102}}{6} when ± is minus.

$$x=-\frac{2\sqrt{102}}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{102}}{3} x=-\frac{2\sqrt{102}}{3}$$