7,5*10^5=(9*10^9*(3.6*10^-6))/(x^2-0,0625)

Solution for 7,5*10^5=(9*10^9*(3.6*10^-6))/(x^2-0,0625) equation:

7.5*10^5=(9*10^9(3.6*10^-6))/(x^2-0.0625)

We move all terms to the left:

7.5*10^5-((9*10^9(3.6*10^-6))/(x^2-0.0625))=0


Domain of the equation: (x^2-0.0625))!=0

x∈R


We add all the numbers together, and all the variables

-((9*10^9(3.6*10^-6))/(x^2-0.0625))+750000=0

We multiply all the terms by the denominator


-((9*10^9(3.6*10^-6))+750000*(x^2-0.0625))=0


We calculate terms in parentheses: -((9*10^9(3.6*10^-6))+750000*(x^2-0.0625)), so:

(9*10^9(3.6*10^-6))+750000*(x^2-0.0625)

determiningTheFunctionDomain
750000*(x^2-0.0625)+(9*10^9(3.6*10^-6))

We add all the numbers together, and all the variables

750000*(x^2-0.0625)+32400

We multiply parentheses

750000x^2-46875+32400

We add all the numbers together, and all the variables

750000x^2-14475

Back to the equation:

-(750000x^2-14475)


We get rid of parentheses

-750000x^2+14475=0

a = -750000; b = 0; c = +14475;
Δ = b2-4ac
Δ = 02-4·(-750000)·14475
Δ = 43425000000
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:

$\sqrt{\Delta}=\sqrt{43425000000}=\sqrt{225000000*193}=\sqrt{225000000}*\sqrt{193}=15000\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-15000\sqrt{193}}{2*-750000}=\frac{0-15000\sqrt{193}}{-1500000}
=-\frac{15000\sqrt{193}}{-1500000}
=-\frac{\sqrt{193}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+15000\sqrt{193}}{2*-750000}=\frac{0+15000\sqrt{193}}{-1500000}
=\frac{15000\sqrt{193}}{-1500000}
=\frac{\sqrt{193}}{-100}
$