-3x+30/x=20

Solution for -3x+30/x=20 equation:

-3x+30/x=20

We move all terms to the left:

-3x+30/x-(20)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


-3x*x-20*x+30=0

We add all the numbers together, and all the variables

-20x-3x*x+30=0

Wy multiply elements

-3x^2-20x+30=0

a = -3; b = -20; c = +30;
Δ = b2-4ac
Δ = -202-4·(-3)·30
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{190}}{2*-3}=\frac{20-2\sqrt{190}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{190}}{2*-3}=\frac{20+2\sqrt{190}}{-6}
$