Question

Escreva as equações na forma
(2x-3)(x+4)-8x=10

Answer 1

$(2x-3)(x+4)-8x=10\to \\\\\\ 2 x^{2} -8x-3x-12-8x-10=0\to \\\\2 x^{2} -19x-10=0\\\\ a=2;b=-19;c=-10\\\\\\ \Delta=b^2-4ac\to \Delta=(-19)^2-4*2*(-10)\to \Delta=361+80\to \\ \Delta=441\\ \\\\x= \frac{-b+- \sqrt{ \Delta} }{2a} \to x= \frac{-(-19)+- \sqrt{ 441} }{2*2} \to x= \frac{19+- 21 }{4} \to \\\\\\ x'= \frac{19+ 21 }{4} \to x'= \frac{40 }{4} \to x'=10\\\\\\ x''= \frac{19- 21 }{4} \to x''= \frac{-2 }{4} \to x''=- \frac{1 }{2}\\\\\\\\ S=(- \frac{1 }{2};10)$