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

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

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

We move all terms to the left:

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


Domain of the equation: 7k!=0

k!=0/7

k!=0

k∈R



Domain of the equation: 2k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


56k^2/126k^2+72k/126k^2+(-315k)/126k^2-4=0

We multiply all the terms by the denominator


56k^2+72k+(-315k)-4*126k^2=0

Wy multiply elements

56k^2-504k^2+72k+(-315k)=0

We get rid of parentheses

56k^2-504k^2+72k-315k=0

We add all the numbers together, and all the variables

-448k^2-243k=0

a = -448; b = -243; c = 0;
Δ = b2-4ac
Δ = -2432-4·(-448)·0
Δ = 59049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{59049}=243$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-243)-243}{2*-448}=\frac{0}{-896}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-243)+243}{2*-448}=\frac{486}{-896}
=-243/448
$