b)
[tex]x^2-5x+9=63-(x-3)(x+3)\\x^2-5x+9=63-(x^2-3^2)\\x^2-5x+9=63-x^2+9\\x^2-5x+9-63+x^2-9=0\\2x^2-5x-63=0\\\Delta=(-5)^2-4*2*(-63)\\\Delta=25+504\\\Delta=529\\\\\sqrt{\Delta}=23\\x_1=\frac{-b-\sqrt{\Delta}}{2a}\\x_1=\frac{-(-5)-23}{2*2}=\frac{5-23}{4}=\frac{-18}4=-\frac{9}2\\\\x_2=\frac{-b+\sqrt{\Delta}}{2a}\\x_2=\frac{-(-5)+23}{2*2}=\frac{5+23}{4}=\frac{28}4=7[/tex]
d)
[tex]6-(1-x)^2=(2x-3)^2-(3x+2)^2\\6-(1^2-2x+x^2)=(4x^2-12x+9)-(9x^2-12x+4)\\6-(1-2x+x^2)=4x^2-12x+9-9x^2+12x-4\\6-1+2x-x^2=4x^2-12x+9-9x^2+12x-4\\\\2x-x^2-4x^2+12x-9x^2+12x=9-4-6+1\\-14x^2+26x=0\\\\\Delta=26^2-4*(-14)*0\\\Delta=676\\\sqrt{\Delta}=26\\\\x_1=\frac{-26-26}{2*(-14)}=\frac{-52}{-28}=\frac{52}{28}=\frac{13}{7}\\x_2=\frac{-26+26}{2*(-14)}=0[/tex]
f)
[tex](2x-3)(3x+5)=(3-2x)(x+3)\\6x^2+10x-9x-15=3x+9-2x^2-6x\\6x^2+10x-9x-15-3x-9+2x^2+6x=0\\8x^2+4x-24=0\\\\\Delta=4^2-4*8*(-24)\\\Delta=16+768\\\Delta=784\\\sqrt{\Delta}=28\\\\x_1=\frac{-4-28}{2*8}=\frac{-32}{16}=-2\\x_2=\frac{-4+28}{2*8}=\frac{24}{16}=\frac{3}{2}[/tex]
