Question

5x²+4x+3=0 solve for x​

Answer 1

Answer:

${ \underline{ \sf{x \: is \: \: \{ \frac{ - 5 + i \sqrt{35} }{10} \} } \: \: and \: \: \{ \frac{ - 5 - i \sqrt{35} }{10} \}} }$

Step-by-step explanation:

$5 {x}^{2} + 4x + 3 = 0$

from quadratic formular:

${ \sf{x = \frac{ - b± \sqrt{ {b}^{2} - 4ac } }{2a} }}$

general equation:

${ax}^{2} + bx + c = 0$

a is 5, b is 4 and c is 3:

substitute in formular:

${ \sf{x = \frac{ - 5± \sqrt{ {5}^{2} - (4 \times 5 \times 3) } }{(2 \times 5)} }} \\ \\ { \sf{x = \frac{ - 5± \sqrt{ - 35} }{10} }}$

but from complexes, i² = -1

${ \sf{x = \frac{ - 5± \sqrt{35 {i}^{2} } }{10} }} \\ \\ = { \sf{x = \frac{ - 5±i \sqrt{35} }{10} }}$