12x/x+33x=75/3

Solution for 12x/x+33x=75/3 equation:

12x/x+33x=75/3

We move all terms to the left:

12x/x+33x-(75/3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

12x/x+33x-25=0

We add all the numbers together, and all the variables

33x+12x/x-25=0

We multiply all the terms by the denominator


33x*x+12x-25*x=0

We add all the numbers together, and all the variables

-13x+33x*x=0

Wy multiply elements

33x^2-13x=0

a = 33; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·33·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*33}=\frac{0}{66}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*33}=\frac{26}{66}
=13/33
$