5/7k-7/5k=-12/35

Solution for 5/7k-7/5k=-12/35 equation:

5/7k-7/5k=-12/35

We move all terms to the left:

5/7k-7/5k-(-12/35)=0


Domain of the equation: 7k!=0

k!=0/7

k!=0

k∈R



Domain of the equation: 5k!=0

k!=0/5

k!=0

k∈R


We get rid of parentheses

5/7k-7/5k+12/35=0

We calculate fractions


2100k^2/3675k^2+2625k/3675k^2+(-5145k)/3675k^2=0

We multiply all the terms by the denominator


2100k^2+2625k+(-5145k)=0

We get rid of parentheses

2100k^2+2625k-5145k=0

We add all the numbers together, and all the variables

2100k^2-2520k=0

a = 2100; b = -2520; c = 0;
Δ = b2-4ac
Δ = -25202-4·2100·0
Δ = 6350400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6350400}=2520$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2520)-2520}{2*2100}=\frac{0}{4200}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2520)+2520}{2*2100}=\frac{5040}{4200}
=1+1/5
$