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

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

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

We move all terms to the left:

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


Domain of the equation: 2k!=0

k!=0/2

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

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

We get rid of parentheses

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

We calculate fractions


(-196k^2)/350k^2+(-1225k)/350k^2+200k/350k^2-3=0

We multiply all the terms by the denominator


(-196k^2)+(-1225k)+200k-3*350k^2=0

We add all the numbers together, and all the variables

(-196k^2)+200k+(-1225k)-3*350k^2=0

Wy multiply elements

(-196k^2)-1050k^2+200k+(-1225k)=0

We get rid of parentheses

-196k^2-1050k^2+200k-1225k=0

We add all the numbers together, and all the variables

-1246k^2-1025k=0

a = -1246; b = -1025; c = 0;
Δ = b2-4ac
Δ = -10252-4·(-1246)·0
Δ = 1050625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1050625}=1025$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1025)-1025}{2*-1246}=\frac{0}{-2492}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1025)+1025}{2*-1246}=\frac{2050}{-2492}
=-1025/1246
$