2/3x+6/5x=15

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

2/3x+6/5x=15

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We calculate fractions


10x/15x^2+18x/15x^2-15=0

We multiply all the terms by the denominator


10x+18x-15*15x^2=0

We add all the numbers together, and all the variables

28x-15*15x^2=0

Wy multiply elements

-225x^2+28x=0

a = -225; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-225)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-225}=\frac{-56}{-450}
=28/225
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-225}=\frac{0}{-450}
=0
$