Question

Ajutatima va rog
Sa se rezolve in R ecuatia
(3x-2)(x-3)=20

Answer 1

3x²-9x-2x+6=20
3x²-11x+6=20
3x²-11x+6-20=0
3x²-11x-14=0. folosim ax²+bx+c=0.
x=11-17 t.s. 6
x=14/3
x=-1

Answer 2

$\displaystyle \mathtt{(3x-2)(x-3)=20}\\ \\ \mathtt{3x^2-9x-2x+6=20}\\ \\ \mathtt{3x^2-11x+6-20=0}\\ \\ \mathtt{3x^2-11x-14=0}\\ \\ \mathtt{a=3,~b=-11,~c=-14}\\ \\ \mathtt{\Delta=b^2-4ac=(-11)^2-4 \cdot 3 \cdot (-14)=121+168=289\ \textgreater \ 0}\\ \\ \mathtt{x_1= \frac{-b+ \sqrt{\Delta} }{2a} = \frac{-(-11)+ \sqrt{289} }{2 \cdot 3} = \frac{11+17}{6}= \frac{28}{6}= \frac{14}{3}}\\ \\ \mathtt{x_2= \frac{-b- \sqrt{\Delta} }{2a} = \frac{-(-11)- \sqrt{289} }{2 \cdot 3}= \frac{11-17}{6}= \frac{-6}{6}=-1 }$