Question

2x ao quadrado -5x=+3x-8

Answer 1

2x^2 -5x = 3x-8

Juntando os semelhantes e igualando a zero:

2x^2 -5x -3x+8 = 0
2x^2 -8x + 8 = 0

Encontrando o Delta, onde:

a = 2, b = -8, c = 8

Delta = b^2 -4.a.c
Delta = (-8)^2 -4.2.8
Delta = 64 - 64
Delta = 0

Quando Delta = 0, a equação possui raízes iguais.

Aplicando a fórmula de Bháskara:

x = -b +/- raiz de delta / 2.a
x = 8 +/- raiz de 0 / 2.2
x = 8 +/- 0 / 4

x' = 8+0 / 4 = 8 / 4 = 2
x'' = 8-0 / 4 = 8 / 4 = 2

S = {2}

:))

Answer 2

$2 x^{2} -5x=+3x-8\\\\\\ 2 x^{2} -5x-3x+8=0\to\\\\ 2 x^{2} -8x+8=0\\\\ a=2;b=-8;c=8\\\\\\ \Delta=b^2-4ac\to \Delta=(-8)^2-4*2*8\to \Delta=64-64\to \Delta=0\\\\\\x'=x''\\\\\\ x= \frac{-b\pm \sqrt{\Delta} }{2a} \to x= \frac{-(-8)\pm \sqrt{0} }{2*2} \to x= \frac{8\pm 0 }{4} \to \\\\\\ x'=x''= \frac{8 }{4} \to x'=x''=2\\\\\\\\ S=(2)$