7/3x+4/6x=45/9

Solution for 7/3x+4/6x=45/9 equation:

7/3x+4/6x=45/9

We move all terms to the left:

7/3x+4/6x-(45/9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

7/3x+4/6x-5=0

We calculate fractions


42x/18x^2+12x/18x^2-5=0

We multiply all the terms by the denominator


42x+12x-5*18x^2=0

We add all the numbers together, and all the variables

54x-5*18x^2=0

Wy multiply elements

-90x^2+54x=0

a = -90; b = 54; c = 0;
Δ = b2-4ac
Δ = 542-4·(-90)·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54}{2*-90}=\frac{-108}{-180}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54}{2*-90}=\frac{0}{-180}
=0
$