0,5x+8/x=-0,8x+13

Solution for 0,5x+8/x=-0,8x+13 equation:

0.5x+8/x=-0.8x+13

We move all terms to the left:

0.5x+8/x-(-0.8x+13)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

0.5x+8/x+0.8x-13=0

We multiply all the terms by the denominator


(0.5x)*x+(0.8x)*x-13*x+8=0

We add all the numbers together, and all the variables

(+0.5x)*x+(+0.8x)*x-13*x+8=0

We add all the numbers together, and all the variables

-13x+(+0.5x)*x+(+0.8x)*x+8=0

We multiply parentheses

0x^2+0x^2-13x+8=0

We add all the numbers together, and all the variables

2x^2-13x+8=0

a = 2; b = -13; c = +8;
Δ = b2-4ac
Δ = -132-4·2·8
Δ = 105
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{-(-13)-\sqrt{105}}{2*2}=\frac{13-\sqrt{105}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{105}}{2*2}=\frac{13+\sqrt{105}}{4}
$