Answer:
[tex]x=-1,\displaystyle \frac{5}{3}[/tex]
Step-by-step explanation:
Hi there!
[tex]6x^2=4x+10[/tex]
Move 6x^2 to the other side of the equation:
[tex]0=-6x^2+4x+10[/tex]
Divide both sides by -2:
[tex]0=3x^2-2x-5[/tex]
Factor by grouping:
[tex]0=3x^2+3x-5x-5\\0=3x(x+1)-5(x+1)\\0=(3x-5)(x+1)[/tex]
Apply the zero product property:
[tex]3x-5 = 0\\3x=5\\\\x=\displaystyle \frac{5}{3}[/tex]
[tex]x+1=0\\x=-1[/tex]
Therefore, x = -1, 5/3.
I hope this helps!
