7/5x+3x=15

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

7/5x+3x=15

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

3x+7/5x-15=0

We multiply all the terms by the denominator


3x*5x-15*5x+7=0

Wy multiply elements

15x^2-75x+7=0

a = 15; b = -75; c = +7;
Δ = b2-4ac
Δ = -752-4·15·7
Δ = 5205
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-\sqrt{5205}}{2*15}=\frac{75-\sqrt{5205}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5205}}{2*15}=\frac{75+\sqrt{5205}}{30}
$