Question

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

Answer 1

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