Help Solve Quadratic Equation 15x^2+24=0

Please Use the factoring to solve the quadratic equation(two possible answers)

15x^2+24=0

Please explain so I can learn and thank you!

I guess your question got problem, should be 15x^2-24=0

15x^2-24=0

move all the numbers to the right side

15x^2=24
x^2=24/15

move the square to the right, which becomes square root

x=(24/15)^0.5

you'll get two answer because square root has positive and negative answer

x1= 1.265
x2= -1.265

15x^2+24=0
x^2 + (24/15)
x^2 = -8/5
x = +/- (-8/5)^(1/2)
= +/- (8(i^2)/5)^(1/2)
= +/- 2i*(2/5)^(1/2)
= +/- (2i/5)* (10^(1/2))

[i^2 = -1]

it is technically wrong to write no solution, but rather no REAL solution as there are two complex number solutions, which are solely "imaginary" (for lack of a better word)

now first out, just see what should be answer looks like...
if 15 times x sq is minus 24 obviously x square is a minus value. therefore in real numbers this has no answer, that is square-root of a minus value.

in complex number system however, you can solve this and get x=1.26i or -0-1.26i

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15x² + 24 = 0
        15x² = -24
           x² = -24/15            ← notice that the left side will always be positive
                                              while the right sides is always negative.
                                              Since positive can never be negative (no matter
                                              what value for x is chosen), there is no solution to this.

           ANSWER
          no solution


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x^2 is either 0 or positive, so there are no real solutions to your equation.

If you want complex answers, x = + - sqrt(-8/5)

unfactorable / no real solutions