4/x+(3/x-45x)=1000

Solution for 4/x+(3/x-45x)=1000 equation:

4/x+(3/x-45x)=1000

We move all terms to the left:

4/x+(3/x-45x)-(1000)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x-45x)!=0

x∈R


We add all the numbers together, and all the variables

4/x+(-45x+3/x)-1000=0

We get rid of parentheses

4/x-45x+3/x-1000=0

We multiply all the terms by the denominator


-45x*x-1000*x+4+3=0

We add all the numbers together, and all the variables

-1000x-45x*x+7=0

Wy multiply elements

-45x^2-1000x+7=0

a = -45; b = -1000; c = +7;
Δ = b2-4ac
Δ = -10002-4·(-45)·7
Δ = 1001260
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:

$\sqrt{\Delta}=\sqrt{1001260}=\sqrt{4*250315}=\sqrt{4}*\sqrt{250315}=2\sqrt{250315}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-2\sqrt{250315}}{2*-45}=\frac{1000-2\sqrt{250315}}{-90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+2\sqrt{250315}}{2*-45}=\frac{1000+2\sqrt{250315}}{-90}
$