Solve 9y^4-29y^2+20=0

$$9 y ^ { 4 } - 29 y ^ { 2 } + 20 = 0$$

Solve for y

$$y = -\frac{2 \sqrt{5}}{3} \approx -1.490711985$$

$$y = \frac{2 \sqrt{5}}{3} \approx 1.490711985$$

$$y=1$$

$$y=-1$$

Steps Using the Quadratic Formula

Substitute t for y^{2}.

$$9t^{2}-29t+20=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 9 for a, -29 for b, and 20 for c in the quadratic formula.

$$t=\frac{-\left(-29\right)±\sqrt{\left(-29\right)^{2}-4\times 9\times 20}}{2\times 9}$$

Do the calculations.

$$t=\frac{29±11}{18}$$

Solve the equation t=\frac{29±11}{18} when ± is plus and when ± is minus.

$$t=\frac{20}{9} t=1$$

Since y=t^{2}, the solutions are obtained by evaluating y=±\sqrt{t} for each t.

$$y=\frac{2\sqrt{5}}{3} y=-\frac{2\sqrt{5}}{3} y=1 y=-1$$