To find roots of a quadratic equation, first try if it could be simply factorized into (x-a) (x-b), so the roots will be x = a or x = b. If it's not easily factorized that way, then, use this quadratic formula:
x = [-b + √(b² - 4ac)] / 2a and
x = [-b - √(b² - 4ac)] / 2a
Now, to use the quadratic formula above, the format of quadratic equation must be in the form of ax²+bx+c = 0
If the quadratic equation is 2x²+32x+119=0, then:
a = 2
b = 32
c = 119
Put a, b, and c values to the formula
x = [-b + √(b² - 4ac)] / 2a
x = [-32 + √(32² - 4*2*119)] / (2*2)
x = [-32 + √(1024 - 952)] / 4
x = (-32 + √72) / 4 --->simplify √72, remember that 72 is 36*2
x = [-32 + √(36*2) ]/ 4 ----> remember that √(a*b) = √a*√b
x = [-32 + (√36*√2)] / 4 --->√36 = 6
x = [-32 + (6*√2)] / 4
x = (-32 + 6√2) / 4
x = -32/4 + (6/4)(√2)
x = -8 + 1.5(√2)
From other quadratic formula, x = [-b - √(b² - 4ac)] / 2a we will have:
x = -8 - 1.5(√2)
If x = p+q(√2), hence:
p = -8
q = 1.5 or q = -1.5