21/4x+11/3x=172

Solution for 21/4x+11/3x=172 equation:

21/4x+11/3x=172

We move all terms to the left:

21/4x+11/3x-(172)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


63x/12x^2+44x/12x^2-172=0

We multiply all the terms by the denominator


63x+44x-172*12x^2=0

We add all the numbers together, and all the variables

107x-172*12x^2=0

Wy multiply elements

-2064x^2+107x=0

a = -2064; b = 107; c = 0;
Δ = b2-4ac
Δ = 1072-4·(-2064)·0
Δ = 11449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11449}=107$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(107)-107}{2*-2064}=\frac{-214}{-4128}
=107/2064
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(107)+107}{2*-2064}=\frac{0}{-4128}
=0
$