(30x^2-14x^2)^1/2=68-10x

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Solution for (30x^2-14x^2)^1/2=68-10x equation: 


x in (-oo:+oo)

((30*x^2-(14*x^2))^1)/2 = 68-(10*x) // - 68-(10*x)

((30*x^2-(14*x^2))^1)/2+10*x-68 = 0

(30*x^2-14*x^2)/2+10*x-68 = 0

(16*x^2)/2+10*x-68 = 0

(16*x^2)/2+(2*10*x)/2+(-68*2)/2 = 0

16*x^2+2*10*x-68*2 = 0

16*x^2+20*x-136 = 0

16*x^2+20*x-136 = 0

4*(4*x^2+5*x-34) = 0

4*x^2+5*x-34 = 0

DELTA = 5^2-(-34*4*4)

DELTA = 569

DELTA > 0

x = (569^(1/2)-5)/(2*4) or x = (-569^(1/2)-5)/(2*4)

x = (569^(1/2)-5)/8 or x = (-(569^(1/2)+5))/8

4*(x+(569^(1/2)+5)/8)*(x-((569^(1/2)-5)/8)) = 0

(4*(x+(569^(1/2)+5)/8)*(x-((569^(1/2)-5)/8)))/2 = 0

(4*(x+(569^(1/2)+5)/8)*(x-((569^(1/2)-5)/8)))/2 = 0 // * 2

4*(x+(569^(1/2)+5)/8)*(x-((569^(1/2)-5)/8)) = 0

( 4 )

4 = 0

x belongs to the empty set

( x+(569^(1/2)+5)/8 )

x+(569^(1/2)+5)/8 = 0 // - (569^(1/2)+5)/8

x = -((569^(1/2)+5)/8)

( x-((569^(1/2)-5)/8) )

x-((569^(1/2)-5)/8) = 0 // + (569^(1/2)-5)/8

x = (569^(1/2)-5)/8

x in { -((569^(1/2)+5)/8), (569^(1/2)-5)/8 }

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