51/2x+2/3x=27

Solution for 51/2x+2/3x=27 equation:

51/2x+2/3x=27

We move all terms to the left:

51/2x+2/3x-(27)=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


153x/6x^2+4x/6x^2-27=0

We multiply all the terms by the denominator


153x+4x-27*6x^2=0

We add all the numbers together, and all the variables

157x-27*6x^2=0

Wy multiply elements

-162x^2+157x=0

a = -162; b = 157; c = 0;
Δ = b2-4ac
Δ = 1572-4·(-162)·0
Δ = 24649
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24649}=157$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(157)-157}{2*-162}=\frac{-314}{-324}
=157/162
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(157)+157}{2*-162}=\frac{0}{-324}
=0
$