Let #color(blue)(y=sinx)#
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#5sin^2 x - 4sinx = 1 =0#
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#rArr5y^2 - 4y - 1 =0#
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This equation is solved by factorizing #" "5y^2 - 4y - 1" "# and
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finding its quadratic roots.
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#delta = b^2 - 4ac = (-4)^2-4(5)(-1) = 16 + 20 = 36#
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#delta>0" "# Two roots exist in #RR#
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#y_1=(-b- sqrt(delta))/(2a)=(4-sqrt36)/(2xx5)=(4-6)/10=-2/10=-1/5#
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#y_2=(-b + sqrt delta)/(2a)=(4+sqrt36)/(2xx5)=(4+6)/10=10/10=1#
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The form of the equation by substituting the factorization form of the polynomial :
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#5y^2 - 4y - 1=0#
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#(y+1/5)(y-1)=0#
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#y+1/5=0rArry=-1/5rArrcolor(blue)(sinx=-1/5)rArrx=-0.2#
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#y-1=0rArry=1rArrcolor(blue)(sinx=1)rArrx=pi/2#
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Hence,#" "x=pi/2" "Or " "x=-0.201358#
