-3x+30/x=12

Solution for -3x+30/x=12 equation:

-3x+30/x=12

We move all terms to the left:

-3x+30/x-(12)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


-3x*x-12*x+30=0

We add all the numbers together, and all the variables

-12x-3x*x+30=0

Wy multiply elements

-3x^2-12x+30=0

a = -3; b = -12; c = +30;
Δ = b2-4ac
Δ = -122-4·(-3)·30
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{14}}{2*-3}=\frac{12-6\sqrt{14}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{14}}{2*-3}=\frac{12+6\sqrt{14}}{-6}
$