17/4x+7/2x=11

Solution for 17/4x+7/2x=11 equation:

17/4x+7/2x=11

We move all terms to the left:

17/4x+7/2x-(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


34x/8x^2+28x/8x^2-11=0

We multiply all the terms by the denominator


34x+28x-11*8x^2=0

We add all the numbers together, and all the variables

62x-11*8x^2=0

Wy multiply elements

-88x^2+62x=0

a = -88; b = 62; c = 0;
Δ = b2-4ac
Δ = 622-4·(-88)·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-62}{2*-88}=\frac{-124}{-176}
=31/44
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+62}{2*-88}=\frac{0}{-176}
=0
$