4.2=x/((0.3-x)(0.4-x))

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Solution for 4.2=x/((0.3-x)(0.4-x)) equation: 


D( x )

(0.3-x)*(0.4-x) = 0

(0.3-x)*(0.4-x) = 0

(0.3-x)*(0.4-x) = 0

( 0.3-x )

0.3-x = 0 // - 0.3

-x = -0.3 // * -1

x = 0.3

( 0.4-x )

0.4-x = 0 // - 0.4

-x = -0.4 // * -1

x = 0.4

x in (-oo:0.3) U (0.3:0.4) U (0.4:+oo)

4.2 = x/((0.3-x)*(0.4-x)) // - x/((0.3-x)*(0.4-x))

4.2-(x/((0.3-x)*(0.4-x))) = 0

(-1*x)/((0.3-x)*(0.4-x))+4.2 = 0

(-1*x)/((0.3-x)*(0.4-x))+(4.2*(0.3-x)*(0.4-x))/((0.3-x)*(0.4-x)) = 0

4.2*(0.3-x)*(0.4-x)-1*x = 0

4.2*x^2-3.94*x+0.504 = 0

4.2*x^2-3.94*x+0.504 = 0

4.2*x^2-3.94*x+0.504 = 0

DELTA = (-3.94)^2-(0.504*4*4.2)

DELTA = 3.94^2-8.4672

DELTA = 7.0564

DELTA > 0

x = ((3.94^2-8.4672)^(1/2)+3.94)/(2*4.2) or x = (3.94-(3.94^2-8.4672)^(1/2))/(2*4.2)

x = 0.11904762*((3.94^2-8.4672)^(1/2)+3.94) or x = 0.11904762*(3.94-(3.94^2-8.4672)^(1/2))

(x-0.11904762*(3.94-(3.94^2-8.4672)^(1/2)))*(x-0.11904762*((3.94^2-8.4672)^(1/2)+3.94)) = 0

((x-0.11904762*(3.94-(3.94^2-8.4672)^(1/2)))*(x-0.11904762*((3.94^2-8.4672)^(1/2)+3.94)))/((0.3-x)*(0.4-x)) = 0

((x-0.11904762*(3.94-(3.94^2-8.4672)^(1/2)))*(x-0.11904762*((3.94^2-8.4672)^(1/2)+3.94)))/((0.3-x)*(0.4-x)) = 0 // * (0.3-x)*(0.4-x)

(x-0.11904762*(3.94-(3.94^2-8.4672)^(1/2)))*(x-0.11904762*((3.94^2-8.4672)^(1/2)+3.94)) = 0

( x-0.11904762*((3.94^2-8.4672)^(1/2)+3.94) )

x-0.11904762*((3.94^2-8.4672)^(1/2)+3.94) = 0 // + -0.11904762*((3.94^2-8.4672)^(1/2)+3.94)

x = -(-0.11904762*((3.94^2-8.4672)^(1/2)+3.94))

x = 0.11904762*((3.94^2-8.4672)^(1/2)+3.94)

( x-0.11904762*(3.94-(3.94^2-8.4672)^(1/2)) )

x-0.11904762*(3.94-(3.94^2-8.4672)^(1/2)) = 0 // + -0.11904762*(3.94-(3.94^2-8.4672)^(1/2))

x = -(-0.11904762*(3.94-(3.94^2-8.4672)^(1/2)))

x = 0.11904762*(3.94-(3.94^2-8.4672)^(1/2))

x in { 0.11904762*((3.94^2-8.4672)^(1/2)+3.94), 0.11904762*(3.94-(3.94^2-8.4672)^(1/2)) }

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