99/x=24.75x2x4

Solution for 99/x=24.75x2x4 equation:

99/x=24.75x^2x4

We move all terms to the left:

99/x-(24.75x^2x4)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

-24.75x^2x4+99/x=0

We multiply all the terms by the denominator


-(24.75x^2x4)*x+99=0

We multiply parentheses

-24x^2+99=0

a = -24; b = 0; c = +99;
Δ = b2-4ac
Δ = 02-4·(-24)·99
Δ = 9504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9504}=\sqrt{144*66}=\sqrt{144}*\sqrt{66}=12\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{66}}{2*-24}=\frac{0-12\sqrt{66}}{-48}
=-\frac{12\sqrt{66}}{-48}
=-\frac{\sqrt{66}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{66}}{2*-24}=\frac{0+12\sqrt{66}}{-48}
=\frac{12\sqrt{66}}{-48}
=\frac{\sqrt{66}}{-4}
$