720*1/x-1.25x=718.75

Solution for 720*1/x-1.25x=718.75 equation:

720*1/x-1.25x=718.75

We move all terms to the left:

720*1/x-1.25x-(718.75)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1.25x+720*1/x-718.75=0

We multiply all the terms by the denominator


-(1.25x)*x-(718.75)*x+720*1=0

We add all the numbers together, and all the variables

-(+1.25x)*x-(718.75)*x+720*1=0

We add all the numbers together, and all the variables

-(+1.25x)*x-(718.75)*x+720=0

We multiply parentheses

-x^2-718.75x+720=0

We add all the numbers together, and all the variables

-1x^2-718.75x+720=0

a = -1; b = -718.75; c = +720;
Δ = b2-4ac
Δ = -718.752-4·(-1)·720
Δ = 519481.5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-718.75)-\sqrt{519481.5625}}{2*-1}=\frac{718.75-\sqrt{519481.5625}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-718.75)+\sqrt{519481.5625}}{2*-1}=\frac{718.75+\sqrt{519481.5625}}{-2}
$