Question

Решите уравнение 10х2=7х+3

Answer 1

10x² = 7x+3

10x²-7x-3 = 0.  a = 10, b = -7, c = -3.

$D = b^2 - 4ac \\ D = (-7)^2 - 4 \cdot10 \cdot (-3) = 49+120 = 169 = 13^2. \ \ \ D \ \textgreater \ 0.$

$x_1_,_2 = \dfrac{-b б \sqrt{D} }{2a}. \\ \\ \\ \\ x_1 = \dfrac{-(-7) + \sqrt{169}}{2 \cdot 10} = \dfrac{7+13}{20} = \dfrac{20}{20} = 1. \\ \\ \\ x_2 = \dfrac{-(-7) - \sqrt{169}}{2 \cdot 10} = \dfrac{7-13}{20} = \dfrac{-6}{20} = -0,3. \\ \\ \\ \boxed{ \boldsymbol{OTBET: \ -0.3;1} }$