5/7k+4=2/2k+3

Solution for 5/7k+4=2/2k+3 equation:

5/7k+4=2/2k+3

We move all terms to the left:

5/7k+4-(2/2k+3)=0


Domain of the equation: 7k!=0

k!=0/7

k!=0

k∈R



Domain of the equation: 2k+3)!=0

k∈R


We get rid of parentheses

5/7k-2/2k-3+4=0

We calculate fractions


10k/14k^2+(-14k)/14k^2-3+4=0

We add all the numbers together, and all the variables

10k/14k^2+(-14k)/14k^2+1=0

We multiply all the terms by the denominator


10k+(-14k)+1*14k^2=0

Wy multiply elements

14k^2+10k+(-14k)=0

We get rid of parentheses

14k^2+10k-14k=0

We add all the numbers together, and all the variables

14k^2-4k=0

a = 14; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·14·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*14}=\frac{0}{28}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*14}=\frac{8}{28}
=2/7
$