3/4x+5/2x=14

Solution for 3/4x+5/2x=14 equation:

3/4x+5/2x=14

We move all terms to the left:

3/4x+5/2x-(14)=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


6x/8x^2+20x/8x^2-14=0

We multiply all the terms by the denominator


6x+20x-14*8x^2=0

We add all the numbers together, and all the variables

26x-14*8x^2=0

Wy multiply elements

-112x^2+26x=0

a = -112; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·(-112)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*-112}=\frac{-52}{-224}
=13/56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*-112}=\frac{0}{-224}
=0
$