9/8k+3/5=3-5/7k

Solution for 9/8k+3/5=3-5/7k equation:

9/8k+3/5=3-5/7k

We move all terms to the left:

9/8k+3/5-(3-5/7k)=0


Domain of the equation: 8k!=0

k!=0/8

k!=0

k∈R



Domain of the equation: 7k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

9/8k-(-5/7k+3)+3/5=0

We get rid of parentheses

9/8k+5/7k-3+3/5=0

We calculate fractions


1176k^2/1400k^2+1575k/1400k^2+1000k/1400k^2-3=0

We multiply all the terms by the denominator


1176k^2+1575k+1000k-3*1400k^2=0

We add all the numbers together, and all the variables

1176k^2+2575k-3*1400k^2=0

Wy multiply elements

1176k^2-4200k^2+2575k=0

We add all the numbers together, and all the variables

-3024k^2+2575k=0

a = -3024; b = 2575; c = 0;
Δ = b2-4ac
Δ = 25752-4·(-3024)·0
Δ = 6630625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6630625}=2575$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2575)-2575}{2*-3024}=\frac{-5150}{-6048}
=2575/3024
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2575)+2575}{2*-3024}=\frac{0}{-6048}
=0
$