Sides of the triangle

Calculate triangle sides where its area is S = 84 cm2 and a = x, b = x + 1, xc = x + 2

Correct result:

a =  13 cm
b =  14 cm
c =  15 cm

Solution:

S=s(s−a)(s−b)(s−c)=84 s=(a+b+c)/2=(3x+3)/2=1.5x+1.5 (1.5x+1.5)(1.5x+1.5−x)(1.5x+1.5−x−1)(1.5x+1.5−x−2)=842 (1.5x+1.5)(0.5x+1.5)(0.5x+0.5)(0.5x−0.5)=7056  0.1875x4+0.75x3+0.375x2−0.75x−7056.56=0  x=13 a=x=13 cm 
b=13+1=14 cm
c=13+2=15 cm

Equation is non-linear.
Equation is not quadratic.
Equation is not cubic.

The real roots of the equation:

x1 = -14.9999987727
x2 = 12.9999987727

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