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Answer 1 · 2017-12-04T11:25:52

See below.

$\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $(-b +-sqrt(b^2-4ac))/(2a)$

Plugging in values:

$\frac{- (- 31) \pm \sqrt{{(- 31)}^{2} - (4 (20) (12))}}{2 (20)}$ $(-(-31)+-sqrt((-31)^2-(4(20)(12))))/(2(20))$

$\frac{31 \pm \sqrt{(961) - (960)}}{40}$ $(31+-sqrt((961)-(960)))/(40)$

$\frac{31 \pm \sqrt{(1)}}{40} \Rightarrow x = \frac{4}{5} and x = \frac{3}{4}$ $(31+-sqrt((1)))/(40)=>x=4/5 and x=3/4$

These are sine ratios, so we need:

${sin}^{- 1} (\frac{4}{5}) = 0.92730$ $sin^-1(4/5)=0.92730$

For: $0 \leq x < 2 π$ $0<= x <2pi$

$0.92730, π - 0.9273 = 2.2143$ $0.92730, pi-0.9273=2.2143$

${sin}^{- 1} (\frac{3}{4}) = 0.84806$ $sin^-1(3/4)=0.84806$

$0.84806, π - 0.84806 = 2.2935$ $0.84806, pi-0.84806=2.2935$

So solutions are:

$0.9273, 2.2143, 0.8481, 2.2935$ $color(blue)(0.9273 , 2.2143 ,0.8481 , 2.2935$