Solve 26y^2=48

$$26 y ^ { 2 } = 48$$

Solve for y

$$y = \frac{2 \sqrt{78}}{13} \approx 1.358732441$$

$$y = -\frac{2 \sqrt{78}}{13} \approx -1.358732441$$

Steps by Finding Square Root

Divide both sides by 26.

$$y^{2}=\frac{48}{26}$$

Reduce the fraction \frac{48}{26} to lowest terms by extracting and canceling out 2.

$$y^{2}=\frac{24}{13}$$

Take the square root of both sides of the equation.

$$y=\frac{2\sqrt{78}}{13} y=-\frac{2\sqrt{78}}{13}$$

Steps Using the Quadratic Formula

Divide both sides by 26.

$$y^{2}=\frac{48}{26}$$

Reduce the fraction \frac{48}{26} to lowest terms by extracting and canceling out 2.

$$y^{2}=\frac{24}{13}$$

Subtract \frac{24}{13} from both sides.

$$y^{2}-\frac{24}{13}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{24}{13} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\left(-\frac{24}{13}\right)}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\left(-\frac{24}{13}\right)}}{2}$$

Multiply -4 times -\frac{24}{13}.

$$y=\frac{0±\sqrt{\frac{96}{13}}}{2}$$

Take the square root of \frac{96}{13}.

$$y=\frac{0±\frac{4\sqrt{78}}{13}}{2}$$

Now solve the equation y=\frac{0±\frac{4\sqrt{78}}{13}}{2} when ± is plus.

$$y=\frac{2\sqrt{78}}{13}$$

Now solve the equation y=\frac{0±\frac{4\sqrt{78}}{13}}{2} when ± is minus.

$$y=-\frac{2\sqrt{78}}{13}$$

The equation is now solved.

$$y=\frac{2\sqrt{78}}{13} y=-\frac{2\sqrt{78}}{13}$$