Solve 4x^2+3x^2-9=0

$$4 x ^ { 2 } + 3 x ^ { 2 } - 9 = 0$$

Solve for x

$$x = \frac{3 \sqrt{7}}{7} \approx 1.133893419$$

$$x = -\frac{3 \sqrt{7}}{7} \approx -1.133893419$$

Steps by Finding Square Root

Combine 4x^{2} and 3x^{2} to get 7x^{2}.

$$7x^{2}-9=0$$

Add 9 to both sides. Anything plus zero gives itself.

$$7x^{2}=9$$

Divide both sides by 7.

$$x^{2}=\frac{9}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{3\sqrt{7}}{7} x=-\frac{3\sqrt{7}}{7}$$

Steps Using the Quadratic Formula

Combine 4x^{2} and 3x^{2} to get 7x^{2}.

$$7x^{2}-9=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, 0 for b, and -9 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 7\left(-9\right)}}{2\times 7}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 7\left(-9\right)}}{2\times 7}$$

Multiply -4 times 7.

$$x=\frac{0±\sqrt{-28\left(-9\right)}}{2\times 7}$$

Multiply -28 times -9.

$$x=\frac{0±\sqrt{252}}{2\times 7}$$

Take the square root of 252.

$$x=\frac{0±6\sqrt{7}}{2\times 7}$$

Multiply 2 times 7.

$$x=\frac{0±6\sqrt{7}}{14}$$

Now solve the equation x=\frac{0±6\sqrt{7}}{14} when ± is plus.

$$x=\frac{3\sqrt{7}}{7}$$

Now solve the equation x=\frac{0±6\sqrt{7}}{14} when ± is minus.

$$x=-\frac{3\sqrt{7}}{7}$$

The equation is now solved.

$$x=\frac{3\sqrt{7}}{7} x=-\frac{3\sqrt{7}}{7}$$