Question

Solve the equation (8-3x)(5x-x)=(3x-4)(x-6)-13

Answer 1

$(8-3x)(5x-x)=(3x-4)(x-6)-13\\ \\ \Rightarrow(8-3x) \times 4x=(3x-4)(x-6)-13\\ \\ \Rightarrow32x-12 x^{2} =3 x^{2} -22x+24-13\\ \\ \Rightarrow 3x^2+12x^2-22x-32x+24-13=0\\ \\ \Rightarrow 15x^2-54x+11=0\\ \\ \Rightarrow x= \frac{-(-54) \pm \sqrt{54^2-4 \times 15 \times 11} }{2 \times 15} \\ \\ \Rightarrow x= \frac{54 \pm \sqrt{2256} }{30}\\ \\ \Rightarrow x= \frac{54+ \sqrt{2256} }{30}\ \ \ and\ \ \ \ \frac{54 - \sqrt{2256} }{30}$