Given eq'n is ax² + b*x +c = 0
The quadratic Equation formula is x = -b ± √(b² - 4ac) / 2a
1. x² + 7x + 12 = 0
By using the above formula
Here a = 1, b = 7, c = 12
x = -7 ± √(7² - 4*1*12) / 2*1
x = -7 ± √(49 - 48) / 2
x = -7 ± √1 / 2
x = -7 ±1 /2
x = -7+1 /2 x = -7 - 1 / 2
x = - 6 / 2 x = -8 / 2
x = -3 x = -4
2) x²-12x+21=0
By using the above formula
Here a = 1, b = -12, c = 21
x = -(-12) ± √((-12)² - 4*1*21) / 2*1
x = 12 ± √(144 - 84) / 2
x = 12 ± √60 / 2
x = 12 ±2√15 /2
x = 12 + 2√15 /2 x = 12 - 2√15 / 2
x = 6 + √15 x = 6 - √15
3. 18+6y-y²=0
By using the above formula
Here a = -1, b = 6, c = 18
x = -6 ± √((6² - 4*(-1)*18) / 2*(-1)
x = -6 ± √(36 + 72) / -2
x = -6 ± √108 / -2
x = -6 ± 6√3 / -2
x = -6+6√3 /-2 x = -6 - 6√3 / -2
x = 3-3√3 x = 3 + 3√3
4. 3x²+14×+15=0
By using the above formula
Here a = 3, b = 14, c = 15
x = -14 ± √((14² - 4*(3)*15) / 2*(3)
x = -14 ± √(196 - 180) / 6
x = -14 ± √16 / 6
x = -14 ± 4 / 6
x = -14 + 4 /6 x = -14 - 4 / 6
x = -10 / 6 x = -18 / 6
x = -5/3 x = -3
5.5x²-18x+12=0
By using the above formula
Here a = 5, b = -18, c = 12
x = -18 ± √((18² - 4*(5)*12) / 2*(5)
x = -18 ± √(324 - 240) / 10
x = -18 ± √84 / 10
x = -18 ± 2√21 / 10
x = -18 + 2√21 /10 x = -18 - 2√21 / 10
x = -9 + √21 / 5 x = -9 - √21 / 5
To learn more about quadratic equations refer below
https://brainly.com/question/17177510
