3/2x+9/8x=14

Solution for 3/2x+9/8x=14 equation:

3/2x+9/8x=14

We move all terms to the left:

3/2x+9/8x-(14)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We calculate fractions


24x/16x^2+18x/16x^2-14=0

We multiply all the terms by the denominator


24x+18x-14*16x^2=0

We add all the numbers together, and all the variables

42x-14*16x^2=0

Wy multiply elements

-224x^2+42x=0

a = -224; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-224)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*-224}=\frac{-84}{-448}
=3/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-224}=\frac{0}{-448}
=0
$