Question

5x²+4x+3=0 solve for x​

Answer 1

`{ \underline{ \sf{x \: is \: \: \{ ( - 5 + i √(35) )/(10) \} } \: \: and \: \: \{ ( - 5 - i √(35) )/(10) \}} }`

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 * 5 * 3) } }{(2 * 5)} }} \\ \\ { \sf{x = ( - 5± √( - 35) )/(10) }}`

but from complexes, i² = -1

`{ \sf{x = \frac{ - 5± \sqrt{35 {i}^(2) } }{10} }} \\ \\ = { \sf{x = ( - 5±i √(35) )/(10) }}`