1/5(x)+1/7(x)=12

Solution for 1/5(x)+1/7(x)=12 equation:

1/5(x)+1/7(x)=12

We move all terms to the left:

1/5(x)+1/7(x)-(12)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We calculate fractions


7x/35x^2+5x/35x^2-12=0

We multiply all the terms by the denominator


7x+5x-12*35x^2=0

We add all the numbers together, and all the variables

12x-12*35x^2=0

Wy multiply elements

-420x^2+12x=0

a = -420; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-420)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-420}=\frac{-24}{-840}
=1/35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-420}=\frac{0}{-840}
=0
$