5/5x+1+7/3x+1=18

Solution for 5/5x+1+7/3x+1=18 equation:

5/5x+1+7/3x+1=18

We move all terms to the left:

5/5x+1+7/3x+1-(18)=0


Domain of the equation: 5x!=0

x!=0/5

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

5/5x+7/3x-16=0

We calculate fractions


15x/15x^2+35x/15x^2-16=0

We multiply all the terms by the denominator


15x+35x-16*15x^2=0

We add all the numbers together, and all the variables

50x-16*15x^2=0

Wy multiply elements

-240x^2+50x=0

a = -240; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·(-240)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-50}{2*-240}=\frac{-100}{-480}
=5/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*-240}=\frac{0}{-480}
=0
$