91=258/x+2.5x

Solution for 91=258/x+2.5x equation:

91=258/x+2.5x

We move all terms to the left:

91-(258/x+2.5x)=0


Domain of the equation: x+2.5x)!=0

x∈R


We add all the numbers together, and all the variables

-(+2.5x+258/x)+91=0

We get rid of parentheses

-2.5x-258/x+91=0

We multiply all the terms by the denominator


-(2.5x)*x+91*x-258=0

We add all the numbers together, and all the variables

-(+2.5x)*x+91*x-258=0

We add all the numbers together, and all the variables

91x-(+2.5x)*x-258=0

We multiply parentheses

-2x^2+91x-258=0

a = -2; b = 91; c = -258;
Δ = b2-4ac
Δ = 912-4·(-2)·(-258)
Δ = 6217
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{-(91)-\sqrt{6217}}{2*-2}=\frac{-91-\sqrt{6217}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+\sqrt{6217}}{2*-2}=\frac{-91+\sqrt{6217}}{-4}
$