Solve 2(2x^2-5)=3left(2-3x^2right)

$$2(2 { x }^{ 2 } -5) = 3 \left( 2-3 { x }^{ 2 } \right)$$

Solve for x

$$x = \frac{4 \sqrt{13}}{13} \approx 1.109400392$$

$$x = -\frac{4 \sqrt{13}}{13} \approx -1.109400392$$

Steps by Finding Square Root

Use the distributive property to multiply 2 by 2x^{2}-5.

$$4x^{2}-10=3\left(2-3x^{2}\right)$$

Use the distributive property to multiply 3 by 2-3x^{2}.

$$4x^{2}-10=6-9x^{2}$$

Add 9x^{2} to both sides.

$$4x^{2}-10+9x^{2}=6$$

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

$$13x^{2}-10=6$$

Add 10 to both sides.

$$13x^{2}=6+10$$

Add 6 and 10 to get 16.

$$13x^{2}=16$$

Divide both sides by 13.

$$x^{2}=\frac{16}{13}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{13}}{13} x=-\frac{4\sqrt{13}}{13}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2 by 2x^{2}-5.

$$4x^{2}-10=3\left(2-3x^{2}\right)$$

Use the distributive property to multiply 3 by 2-3x^{2}.

$$4x^{2}-10=6-9x^{2}$$

Subtract 6 from both sides.

$$4x^{2}-10-6=-9x^{2}$$

Subtract 6 from -10 to get -16.

$$4x^{2}-16=-9x^{2}$$

Add 9x^{2} to both sides.

$$4x^{2}-16+9x^{2}=0$$

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

$$13x^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 13 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 13\left(-16\right)}}{2\times 13}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 13\left(-16\right)}}{2\times 13}$$

Multiply -4 times 13.

$$x=\frac{0±\sqrt{-52\left(-16\right)}}{2\times 13}$$

Multiply -52 times -16.

$$x=\frac{0±\sqrt{832}}{2\times 13}$$

Take the square root of 832.

$$x=\frac{0±8\sqrt{13}}{2\times 13}$$

Multiply 2 times 13.

$$x=\frac{0±8\sqrt{13}}{26}$$

Now solve the equation x=\frac{0±8\sqrt{13}}{26} when ± is plus.

$$x=\frac{4\sqrt{13}}{13}$$

Now solve the equation x=\frac{0±8\sqrt{13}}{26} when ± is minus.

$$x=-\frac{4\sqrt{13}}{13}$$

The equation is now solved.

$$x=\frac{4\sqrt{13}}{13} x=-\frac{4\sqrt{13}}{13}$$