Solve 25*3=8*y^2

$$25 \times 3 = 8 \times y ^ { 2 }$$

Solve for y

$$y = \frac{5 \sqrt{6}}{4} \approx 3.061862178$$

$$y = -\frac{5 \sqrt{6}}{4} \approx -3.061862178$$

Steps by Finding Square Root

Multiply 25 and 3 to get 75.

$$75=8y^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$8y^{2}=75$$

Divide both sides by 8.

$$y^{2}=\frac{75}{8}$$

Take the square root of both sides of the equation.

$$y=\frac{5\sqrt{6}}{4} y=-\frac{5\sqrt{6}}{4}$$

Steps Using the Quadratic Formula

Multiply 25 and 3 to get 75.

$$75=8y^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$8y^{2}=75$$

Subtract 75 from both sides.

$$8y^{2}-75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 8\left(-75\right)}}{2\times 8}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 8\left(-75\right)}}{2\times 8}$$

Multiply -4 times 8.

$$y=\frac{0±\sqrt{-32\left(-75\right)}}{2\times 8}$$

Multiply -32 times -75.

$$y=\frac{0±\sqrt{2400}}{2\times 8}$$

Take the square root of 2400.

$$y=\frac{0±20\sqrt{6}}{2\times 8}$$

Multiply 2 times 8.

$$y=\frac{0±20\sqrt{6}}{16}$$

Now solve the equation y=\frac{0±20\sqrt{6}}{16} when ± is plus.

$$y=\frac{5\sqrt{6}}{4}$$

Now solve the equation y=\frac{0±20\sqrt{6}}{16} when ± is minus.

$$y=-\frac{5\sqrt{6}}{4}$$

The equation is now solved.

$$y=\frac{5\sqrt{6}}{4} y=-\frac{5\sqrt{6}}{4}$$