-8/5k+4/7=3-1/2k

Solution for -8/5k+4/7=3-1/2k equation:

-8/5k+4/7=3-1/2k

We move all terms to the left:

-8/5k+4/7-(3-1/2k)=0


Domain of the equation: 5k!=0

k!=0/5

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

-8/5k-(-1/2k+3)+4/7=0

We get rid of parentheses

-8/5k+1/2k-3+4/7=0

We calculate fractions


80k^2/490k^2+(-784k)/490k^2+245k/490k^2-3=0

We multiply all the terms by the denominator


80k^2+(-784k)+245k-3*490k^2=0

We add all the numbers together, and all the variables

80k^2+245k+(-784k)-3*490k^2=0

Wy multiply elements

80k^2-1470k^2+245k+(-784k)=0

We get rid of parentheses

80k^2-1470k^2+245k-784k=0

We add all the numbers together, and all the variables

-1390k^2-539k=0

a = -1390; b = -539; c = 0;
Δ = b2-4ac
Δ = -5392-4·(-1390)·0
Δ = 290521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{290521}=539$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-539)-539}{2*-1390}=\frac{0}{-2780}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-539)+539}{2*-1390}=\frac{1078}{-2780}
=-539/1390
$