8/x+5=3x-5

Solution for 8/x+5=3x-5 equation:

8/x+5=3x-5

We move all terms to the left:

8/x+5-(3x-5)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

8/x-3x+5+5=0

We multiply all the terms by the denominator


-3x*x+5*x+5*x+8=0

We add all the numbers together, and all the variables

10x-3x*x+8=0

Wy multiply elements

-3x^2+10x+8=0

a = -3; b = 10; c = +8;
Δ = b2-4ac
Δ = 102-4·(-3)·8
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-14}{2*-3}=\frac{-24}{-6}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+14}{2*-3}=\frac{4}{-6}
=-2/3
$