Please help me solve this problem and explain why so I can understand if you can please

Solve and explain, that's what we're here for.

We're asked for the intersection of a line and a parabola; there may be zero, one or two intersections.  We can write the quadratic and examine its discriminant.

x = 2y + 5

It's probably easier if we do y as a function of x.

x - 5 = 2y

y = (x-5)/2

That's equal to

y = (2x - 3)(x + 9)

(x-5)/2 = 2x² + 15x - 27

x - 5 = 4x² + 30x - 54

0 = 4x² + 29x - 49

Discriminant is d=b²-4ac = 29² - 4(4)(-49).  Since ac<0 we get d>0 so two solutions.

C) 2

We could solve the equation with the quadratic formula but they didn't ask so we won't.

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

2x

2

=

10

2

x=5

step-by-step explanation: