Question

6x²=5x+11
x(x-1)=72
2x(x+2)=8x+3​

Answer 1

$6x^2=5x+11\\\\6x^2-5x-11=0\\\\D=(-5)^2-4*6*(-11)=25+264=289\\\\x_1=\frac{5+\sqrt{289} }{2*6}=\frac{5+17}{12}=\frac{22}{12}=\frac{11}{6}=1\frac{5}{6} \\\\x_2=\frac{5-\sqrt{289} }{2*6}=\frac{5-17}{12}=\frac{-12}{12}=-1\\\\x_1=1\frac{5}{6};\\ \\x_2=-1$

$x(x-1)=72\\\\x^2-x=72\\\\x^2-x-72=0\\\\D=(-1)^2-4*1*(-72)=1+288=289\\\\x_1=\frac{1+\sqrt{289} }{2*1}=\frac{1+17}{2}=\frac{18}{2}=9\\\\x_2=\frac{1-\sqrt{289} }{2*1}=\frac{1-17}{2}=\frac{-16}{2}=-8\\\\x_1=9\\\\x_2=-8$

$2x(x+2)=8x+3\\\\2x^2+4x=8x+3\\\\2x^2+4x-8x-3=0\\\\2x^2-4x-3=0\\\\D=(-4)^2-4*2*(-3)=16+24=40\\\\x_1=\frac{4+\sqrt{40} }{2*2}=\frac{4+\sqrt{40} }{4} \\\\x_2=\frac{4-\sqrt{40} }{2*2}=\frac{4-\sqrt{40} }{4}\\\\x_1=\frac{4+\sqrt{40} }{4} \\\\x_2=\frac{4-\sqrt{40} }{4}$