Question

1)6x^{2}+13x+4=0 2) 5x^{2}+24x+9=0 3) 7x^{2}-27x+12=0 4) 4x^{2}+3x-2=0 5)6x^{2}-10x-1=0

Answer 1

$6x^2+13x+4=0 \\ \delta=13^2-(6*4*4)=169-96=73 \\ x_1= \frac{-b- \sqrt{\delta} }{2a} = \frac{-13- \sqrt{73} }{12} \\ x_2= \frac{-b+ \sqrt{\delta} }{2a} = \frac{-13+ \sqrt{73} }{12}$

$5x^2+24x+9=0 \\ \delta=24^2-(9*5*4)=576-180=396 \\ x_1= \frac{-b- \sqrt{\delta} }{2a} = \frac{-24- \sqrt{396} }{10} \\ x_2= \frac{-b \sqrt{\delta} }{2a} = \frac{-24+ \sqrt{396} }{10}$

$7x^2-27x+12=0 \\ \delta=(-27)^2-(7*12*4)=393 \\ x_1= \frac{27- \sqrt{393} }{14} \\ x_2= \frac{27+ \sqrt{393} }{14}$

$4x^2+3x-2=0 \\ \delta=3^2-(-2*4*4)=9-(-32)=9+32=41 \\ x_1= \frac{-3- \sqrt{41} }{8} \\ x_2= \frac{-3+ \sqrt{41}}{8 }$

$6x^2-10x-1=0 \\ \delta=(-10)^2-(-1*6*4)=100+24=124 \\ x_1= \frac{10- \sqrt{124} }{12} \\ x_2= \frac{10+ \sqrt{124} }{12}$