Question

Which expression gives the solutions of -5+2x^2=-6x

Answer 1

The solutions are

`x1=(-6+2√(19))/(4)`

`x2=\frac{-6-2√(19)} {4}`

Explanation:

we have

`-5+2x^(2) =-6x`

rewrite the quadratic equation

`2x^(2)+6x-5=0`

The formula to solve a quadratic equation of the form
`ax^(2) +bx+c=0` is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`2x^(2)+6x-5=0`

so

`a=2\\b=6\\c=-5`

substitute in the formula

`x=\frac{-6(+/-)\sqrt{6^(2)-4(2)(-5)}} {2(2)}`

`x=\frac{-6(+/-)√(76)} {4}`

`x=\frac{-6(+/-)2√(19)} {4}`

`x1=(-6+2√(19))/(4)`

`x2=\frac{-6-2√(19)} {4}`