7/2x+5/3x=15/6

Solution for 7/2x+5/3x=15/6 equation:

7/2x+5/3x=15/6

We move all terms to the left:

7/2x+5/3x-(15/6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

7/2x+5/3x-(+15/6)=0

We get rid of parentheses

7/2x+5/3x-15/6=0

We calculate fractions


(-270x^2)/216x^2+756x/216x^2+360x/216x^2=0

We multiply all the terms by the denominator


(-270x^2)+756x+360x=0

We add all the numbers together, and all the variables

(-270x^2)+1116x=0

We get rid of parentheses

-270x^2+1116x=0

a = -270; b = 1116; c = 0;
Δ = b2-4ac
Δ = 11162-4·(-270)·0
Δ = 1245456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1245456}=1116$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1116)-1116}{2*-270}=\frac{-2232}{-540}
=4+2/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1116)+1116}{2*-270}=\frac{0}{-540}
=0
$