30x+8/x=-34

Solution for 30x+8/x=-34 equation:

30x+8/x=-34

We move all terms to the left:

30x+8/x-(-34)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

30x+8/x+34=0

We multiply all the terms by the denominator


30x*x+34*x+8=0

We add all the numbers together, and all the variables

34x+30x*x+8=0

Wy multiply elements

30x^2+34x+8=0

a = 30; b = 34; c = +8;
Δ = b2-4ac
Δ = 342-4·30·8
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{-(34)-14}{2*30}=\frac{-48}{60}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+14}{2*30}=\frac{-20}{60}
=-1/3
$