(180x-1800)/(x)(x-20)=4

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Solution for (180x-1800)/(x)(x-20)=4 equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

((180*x-1800)/x)*(x-20) = 4 // - 4

((180*x-1800)/x)*(x-20)-4 = 0

((180*x-1800)*(x-20))/x-4 = 0

((180*x-1800)*(x-20))/x+(-4*x)/x = 0

(180*x-1800)*(x-20)-4*x = 0

180*x^2-5404*x+36000 = 0

180*x^2-5404*x+36000 = 0

4*(45*x^2-1351*x+9000) = 0

45*x^2-1351*x+9000 = 0

DELTA = (-1351)^2-(4*45*9000)

DELTA = 205201

DELTA > 0

x = (205201^(1/2)+1351)/(2*45) or x = (1351-205201^(1/2))/(2*45)

x = (205201^(1/2)+1351)/90 or x = (1351-205201^(1/2))/90

4*(x-((1351-205201^(1/2))/90))*(x-((205201^(1/2)+1351)/90)) = 0

(4*(x-((1351-205201^(1/2))/90))*(x-((205201^(1/2)+1351)/90)))/x = 0

(4*(x-((1351-205201^(1/2))/90))*(x-((205201^(1/2)+1351)/90)))/x = 0 // * x

4*(x-((1351-205201^(1/2))/90))*(x-((205201^(1/2)+1351)/90)) = 0

( x-((1351-205201^(1/2))/90) )

x-((1351-205201^(1/2))/90) = 0 // + (1351-205201^(1/2))/90

x = (1351-205201^(1/2))/90

( x-((205201^(1/2)+1351)/90) )

x-((205201^(1/2)+1351)/90) = 0 // + (205201^(1/2)+1351)/90

x = (205201^(1/2)+1351)/90

x in { (1351-205201^(1/2))/90, (205201^(1/2)+1351)/90 }

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