Solve 9x^2+4x^2=6

$$9 x ^ { 2 } + 4 x ^ { 2 } = 6$$

Solve for x

$$x=\frac{\sqrt{78}}{13}\approx 0.67936622$$

$$x=-\frac{\sqrt{78}}{13}\approx -0.67936622$$

Steps by Finding Square Root

Combine 9x^{2} and 4x^{2} to get 13x^{2}.

$$13x^{2}=6$$

Divide both sides by 13.

$$x^{2}=\frac{6}{13}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{78}}{13} x=-\frac{\sqrt{78}}{13}$$

Steps Using the Quadratic Formula

Combine 9x^{2} and 4x^{2} to get 13x^{2}.

$$13x^{2}=6$$

Subtract 6 from both sides.

$$13x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 13 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 13\left(-6\right)}}{2\times 13}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 13\left(-6\right)}}{2\times 13}$$

Multiply -4 times 13.

$$x=\frac{0±\sqrt{-52\left(-6\right)}}{2\times 13}$$

Multiply -52 times -6.

$$x=\frac{0±\sqrt{312}}{2\times 13}$$

Take the square root of 312.

$$x=\frac{0±2\sqrt{78}}{2\times 13}$$

Multiply 2 times 13.

$$x=\frac{0±2\sqrt{78}}{26}$$

Now solve the equation x=\frac{0±2\sqrt{78}}{26} when ± is plus.

$$x=\frac{\sqrt{78}}{13}$$

Now solve the equation x=\frac{0±2\sqrt{78}}{26} when ± is minus.

$$x=-\frac{\sqrt{78}}{13}$$

The equation is now solved.

$$x=\frac{\sqrt{78}}{13} x=-\frac{\sqrt{78}}{13}$$