Solve 9*{left(3/7yright)}^2-left(2yright)^2=3*(3/7)

$$9 \times { \left( \frac{ 3 }{ 7 } y \right) }^{ 2 } - { \left(2y \right) }^{ 2 } =3 \times ( \frac{ 3 }{ 7 } )$$

Solve for y

$$y=-\frac{3\sqrt{805}i}{115}\approx -0-0.740152746i$$

$$y=\frac{3\sqrt{805}i}{115}\approx 0.740152746i$$

Steps by Finding Square Root

Expand \left(\frac{3}{7}y\right)^{2}.

$$9\times \left(\frac{3}{7}\right)^{2}y^{2}-\left(2y\right)^{2}=3\times \frac{3}{7}$$

Calculate \frac{3}{7} to the power of 2 and get \frac{9}{49}.

$$9\times \frac{9}{49}y^{2}-\left(2y\right)^{2}=3\times \frac{3}{7}$$

Multiply 9 and \frac{9}{49} to get \frac{81}{49}.

$$\frac{81}{49}y^{2}-\left(2y\right)^{2}=3\times \frac{3}{7}$$

Expand \left(2y\right)^{2}.

$$\frac{81}{49}y^{2}-2^{2}y^{2}=3\times \frac{3}{7}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{81}{49}y^{2}-4y^{2}=3\times \frac{3}{7}$$

Combine \frac{81}{49}y^{2} and -4y^{2} to get -\frac{115}{49}y^{2}.

$$-\frac{115}{49}y^{2}=3\times \frac{3}{7}$$

Multiply 3 and \frac{3}{7} to get \frac{9}{7}.

$$-\frac{115}{49}y^{2}=\frac{9}{7}$$

Multiply both sides by -\frac{49}{115}, the reciprocal of -\frac{115}{49}.

$$y^{2}=\frac{9}{7}\left(-\frac{49}{115}\right)$$

Multiply \frac{9}{7} and -\frac{49}{115} to get -\frac{63}{115}.

$$y^{2}=-\frac{63}{115}$$

The equation is now solved.

$$y=\frac{3\sqrt{805}i}{115} y=-\frac{3\sqrt{805}i}{115}$$

Steps Using the Quadratic Formula

Expand \left(\frac{3}{7}y\right)^{2}.

$$9\times \left(\frac{3}{7}\right)^{2}y^{2}-\left(2y\right)^{2}=3\times \frac{3}{7}$$

Calculate \frac{3}{7} to the power of 2 and get \frac{9}{49}.

$$9\times \frac{9}{49}y^{2}-\left(2y\right)^{2}=3\times \frac{3}{7}$$

Multiply 9 and \frac{9}{49} to get \frac{81}{49}.

$$\frac{81}{49}y^{2}-\left(2y\right)^{2}=3\times \frac{3}{7}$$

Expand \left(2y\right)^{2}.

$$\frac{81}{49}y^{2}-2^{2}y^{2}=3\times \frac{3}{7}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{81}{49}y^{2}-4y^{2}=3\times \frac{3}{7}$$

Combine \frac{81}{49}y^{2} and -4y^{2} to get -\frac{115}{49}y^{2}.

$$-\frac{115}{49}y^{2}=3\times \frac{3}{7}$$

Multiply 3 and \frac{3}{7} to get \frac{9}{7}.

$$-\frac{115}{49}y^{2}=\frac{9}{7}$$

Subtract \frac{9}{7} from both sides.

$$-\frac{115}{49}y^{2}-\frac{9}{7}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{115}{49} for a, 0 for b, and -\frac{9}{7} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-\frac{115}{49}\right)\left(-\frac{9}{7}\right)}}{2\left(-\frac{115}{49}\right)}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-\frac{115}{49}\right)\left(-\frac{9}{7}\right)}}{2\left(-\frac{115}{49}\right)}$$

Multiply -4 times -\frac{115}{49}.

$$y=\frac{0±\sqrt{\frac{460}{49}\left(-\frac{9}{7}\right)}}{2\left(-\frac{115}{49}\right)}$$

Multiply \frac{460}{49} times -\frac{9}{7} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$y=\frac{0±\sqrt{-\frac{4140}{343}}}{2\left(-\frac{115}{49}\right)}$$

Take the square root of -\frac{4140}{343}.

$$y=\frac{0±\frac{6\sqrt{805}i}{49}}{2\left(-\frac{115}{49}\right)}$$

Multiply 2 times -\frac{115}{49}.

$$y=\frac{0±\frac{6\sqrt{805}i}{49}}{-\frac{230}{49}}$$

Now solve the equation y=\frac{0±\frac{6\sqrt{805}i}{49}}{-\frac{230}{49}} when ± is plus.

$$y=-\frac{3\sqrt{805}i}{115}$$

Now solve the equation y=\frac{0±\frac{6\sqrt{805}i}{49}}{-\frac{230}{49}} when ± is minus.

$$y=\frac{3\sqrt{805}i}{115}$$

The equation is now solved.

$$y=-\frac{3\sqrt{805}i}{115} y=\frac{3\sqrt{805}i}{115}$$