The given equations are y= 6x^2+1 and y=x^2+4
Both the equations equal y so we can make them equal
6x^2+1=x^2+4
To bring x term on one side we subtract x^2 both sides
6x^2-x^2+1=4
5x^2+1=4
To isolate x term we subtract 1 both sides
5x^2=4-1
5x^2=3
Dividing by 5 both sides
X^2=3/5
Taking root of both sides we have:
X=±√⅗
Substituting x value to find y
When x=+√⅗=0.7745
Y= 6x^2+1
Y=6(3/5)+1
Y= 18/5+1
Y=23/5 =4.6
When x= -√⅗=-0.7745
Y= 6(3/5)+1
Y=23/5=4.6
Point of intersections are ( 0.7745,4.6) and (-0.7745,4.6)
