Solve 3y(y-2)=4-6y

$$3 y ( y - 2 ) = 4 - 6 y$$

Solve for y

$$y = \frac{2 \sqrt{3}}{3} \approx 1.154700538$$

$$y = -\frac{2 \sqrt{3}}{3} \approx -1.154700538$$

Steps by Finding Square Root

Use the distributive property to multiply 3y by y-2.

$$3y^{2}-6y=4-6y$$

Add 6y to both sides.

$$3y^{2}-6y+6y=4$$

Combine -6y and 6y to get 0.

$$3y^{2}=4$$

Divide both sides by 3.

$$y^{2}=\frac{4}{3}$$

Take the square root of both sides of the equation.

$$y=\frac{2\sqrt{3}}{3} y=-\frac{2\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 3y by y-2.

$$3y^{2}-6y=4-6y$$

Subtract 4 from both sides.

$$3y^{2}-6y-4=-6y$$

Add 6y to both sides.

$$3y^{2}-6y-4+6y=0$$

Combine -6y and 6y to get 0.

$$3y^{2}-4=0$$

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

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

Square 0.

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

Multiply -4 times 3.

$$y=\frac{0±\sqrt{-12\left(-4\right)}}{2\times 3}$$

Multiply -12 times -4.

$$y=\frac{0±\sqrt{48}}{2\times 3}$$

Take the square root of 48.

$$y=\frac{0±4\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$y=\frac{0±4\sqrt{3}}{6}$$

Now solve the equation y=\frac{0±4\sqrt{3}}{6} when ± is plus.

$$y=\frac{2\sqrt{3}}{3}$$

Now solve the equation y=\frac{0±4\sqrt{3}}{6} when ± is minus.

$$y=-\frac{2\sqrt{3}}{3}$$

The equation is now solved.

$$y=\frac{2\sqrt{3}}{3} y=-\frac{2\sqrt{3}}{3}$$