Question

(2x+1)^2 -3(x+5)^2=(3-x)(x-3)

Answer 1

$(2x+1)^2-3(x+5)^2=(3-x)(x-3) \\ \\ (4x^2+4x+1)-3(x^2+10x+25)=-(x-3)(x-3) \\ \\ 4x^2+4x+1-3x^2-30x-75=-x^2+6x-9 \\ \\ 4x^2+4x+1-3x^2-30x-75+x^2-6x+9=0 \\ \\ 2x^2-32x-65=0 \\ \\ D= \sqrt{(-32)^2-4*2*(-65)}= \sqrt{1544} =б2 \sqrt{386} \\ \\ x_1= \frac{32+2 \sqrt{386}}{4}= \frac{16+2 \sqrt{386}}{2} \\ \\ x_2= \frac{32-2 \sqrt{386}}{4}= \frac{16-2 \sqrt{386}}{2}$