31/2x+21/4x=6+5

Solution for 31/2x+21/4x=6+5 equation:

31/2x+21/4x=6+5

We move all terms to the left:

31/2x+21/4x-(6+5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

31/2x+21/4x-11=0

We calculate fractions


124x/8x^2+42x/8x^2-11=0

We multiply all the terms by the denominator


124x+42x-11*8x^2=0

We add all the numbers together, and all the variables

166x-11*8x^2=0

Wy multiply elements

-88x^2+166x=0

a = -88; b = 166; c = 0;
Δ = b2-4ac
Δ = 1662-4·(-88)·0
Δ = 27556
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{27556}=166$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(166)-166}{2*-88}=\frac{-332}{-176}
=1+39/44
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(166)+166}{2*-88}=\frac{0}{-176}
=0
$