41/4x+31/2x=11

Solution for 41/4x+31/2x=11 equation:

41/4x+31/2x=11

We move all terms to the left:

41/4x+31/2x-(11)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


82x/8x^2+124x/8x^2-11=0

We multiply all the terms by the denominator


82x+124x-11*8x^2=0

We add all the numbers together, and all the variables

206x-11*8x^2=0

Wy multiply elements

-88x^2+206x=0

a = -88; b = 206; c = 0;
Δ = b2-4ac
Δ = 2062-4·(-88)·0
Δ = 42436
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{42436}=206$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(206)-206}{2*-88}=\frac{-412}{-176}
=2+15/44
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(206)+206}{2*-88}=\frac{0}{-176}
=0
$