2,5x^2+25x-35/x=0

Solution for 2,5x^2+25x-35/x=0 equation:

2.5x^2+25x-35/x=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


(2.5x^2)*x+25x*x-35=0

We multiply parentheses

2x^2+25x*x-35=0

Wy multiply elements

2x^2+25x^2-35=0

We add all the numbers together, and all the variables

27x^2-35=0

a = 27; b = 0; c = -35;
Δ = b2-4ac
Δ = 02-4·27·(-35)
Δ = 3780
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:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{105}}{2*27}=\frac{0-6\sqrt{105}}{54}
=-\frac{6\sqrt{105}}{54}
=-\frac{\sqrt{105}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{105}}{2*27}=\frac{0+6\sqrt{105}}{54}
=\frac{6\sqrt{105}}{54}
=\frac{\sqrt{105}}{9}
$