The y² has a coefficient of 35 and
since we can't factor this 35 out of the equation,
we want to multiply this coefficent with the constant c

Ay² + By - C

35y² + 3y - 2

35(2) = 70

next, we want to find the numbers that can be
multiplied to get 70 and added or subtracted to get 3

here, our numbers are 10 and 7
10(7) = 70   &   10 -7 = 3

now, we'll rewrite the equation using our 10 and 7

35y² + 3y - 2

35y² - 7y + 10y - 2

break the equation in half and factor

quadratic equations

35y2 - 7y 7y(5y - 1)

10y - 2 2(5y - 1)

factoring equations

our equation breaks down to

(7y + 2)(5y - 1)

finally, we can finish this by solving for y₁ & y₂,
also called 'the roots'
this is where the parabola crosses the y-axis

finding real roots

7y + 2 = 0 7y = - 2 y = - 2 / 7

finding real roots

5y - 1 = 0 5y = 1 y = 1 / 5

parabolas