Question

Cum se rezolvă ecuația?
(x+4)-(2x-3)×(x-4)=0

Answer 1

$x + 4 - (2x - 3)(x - 4) = 0$

$x + 4 - (2 {x}^{2} - 8x - 3x + 12) = 0$

$x + 4 - 2 {x}^{2} + 8x + 3x - 12 = 0$

$- 2 {x}^{2} + 12x - 8 = 0 \: | \div ( - 2)$

${x}^{2} - 6x + 4 = 0$

$a = 1$

$b = - 6$

$c = 4$

$\Delta = {b}^{2} - 4ac$

$\Delta = {( - 6)}^{2} - 4 \times 1 \times 4$

$\Delta = 36 - 16$

$\Delta = 20$

$x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a}$

$x_{1,2}=\frac{-( - 6)\pm\sqrt{20}}{2 \times 1}$

$x_{1,2}=\frac{6\pm2\sqrt{5}}{2}$

$x_{1}=\frac{6 + 2\sqrt{5}}{2}$

$x_{1}=\frac{2(3+ \sqrt{5})}{2}$

$x_{1}=3 + \sqrt{5}$

$x_{2}=\frac{6 - 2\sqrt{5}}{2}$

$x_{2}=\frac{2(3 - \sqrt{5})}{2}$

$x_{2}=3 - \sqrt{5}$