The solutions for [tex]-5 +2x^{2} = -6x[/tex] is option 3. [tex]x= \frac{-6 \pm \sqrt{36-4 (2)(-5)}}{4} .[/tex]
Step-by-step explanation:
Step 1:
First, we must bring the equation to the form of [tex]ax^{2} +bx +c =0.[/tex]
So [tex]-5 +2x^{2} = -6x[/tex] becomes [tex]2x^{2} +6x-5=0.[/tex]
The value of a is the coefficient of the [tex]x^{2}[/tex] term, the value of b is the coefficient of x term and c is the coefficient of the constant term.
Comparing the above equation to [tex]ax^{2} +bx +c =0,[/tex] we get [tex]a = 2, b = 6,[/tex] and [tex]c=-5.[/tex]
We have the formula [tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}.[/tex]
Step 2:
By substituting the known values, we get
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a} =\frac{-6 \pm \sqrt{6^{2}-4 (2)(-5)}}{2 (2)}.[/tex]
[tex]\frac{-6 \pm \sqrt{6^{2}-4 (2)(-5)}}{2 (2)} = \frac{-6 \pm \sqrt{36-4 (2)(-5)}}{4} .[/tex]
This is the third option.
