21/2x+12/3x=25

Solution for 21/2x+12/3x=25 equation:

21/2x+12/3x=25

We move all terms to the left:

21/2x+12/3x-(25)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


63x/6x^2+24x/6x^2-25=0

We multiply all the terms by the denominator


63x+24x-25*6x^2=0

We add all the numbers together, and all the variables

87x-25*6x^2=0

Wy multiply elements

-150x^2+87x=0

a = -150; b = 87; c = 0;
Δ = b2-4ac
Δ = 872-4·(-150)·0
Δ = 7569
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7569}=87$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(87)-87}{2*-150}=\frac{-174}{-300}
=29/50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(87)+87}{2*-150}=\frac{0}{-300}
=0
$