how to solve for roots ?

Question

x^2 - 4.5 x -100=0

how to solve it for roots ?

my concern is ....coefficient is 4.5 ......fraction ....so i face difficulty in factoring .

I cant use direct formula x= -b+/ sqrt(b^2-4ac)/2a ..........because its becoming messy .

can anybody suggest some smarter way to solve it ?

Answer 1

The roots are

x1=(-b + sqrt(b^2-4ac))/2a
x2=(-b - sqrt(b^2-4ac))/2a

b^2-4ac = (-4.5)^2 - 4(1) (-100) = 20.25- (-400) = 420.25
Sqrt(b^2-4ac) = sqrt (420.25) = 20.5

=> x1 =( - (-4.5) + 20.5)/2(1) = 12.5
=>x2 = (- (-4.5)- 20.5)/2(1) = -8

so the roots are 12.5 and 8

Answer 2

If you put 4.5 = 9/2 and multiply both sides by 2 the equation becomes
2x^2-9x-200=0 and now apply the direct formula with integral coefficients